Baan CANGA | Cd a s\~ ~@ QUESTION BANK WITH SOLUTIONS 4 / ON | . COMPUTER AIDED ENGINEERING DRAWING : FOR II SEMESTER BE VISVESVARAYA TECHNOLOGICAL UNIVERSITY BELGAUM-590 014 2007CONTENTS Primer Committee Foreword Preface Contents CHAPTER 1: PROJECTIONS OF POINTS CHAPTER 2: PROJECTIONS STRAIGHT LINES CHAPTER 3: PROJECTIONS PLANE SURFACES CHAPTER 4; PROJECTIONS SOLIDS CHAPTER 5: DEVELOPMENT OF LATERAL SURFACES OF SOLIDS CHAPTER 6 : ISOMETRIC PROJECTIONS PAGE No 1 ig vii IV 27 53 7 125 154} CHAPTER 1 PROJECTIONS OF POINTS Problem 1, Draw the projections of the following Points on the same XY tine, keeping convenient distance between ‘each projectors. Name the Quadrants in which they lie. ‘A~ 30 mm above HP & 35 mm in front of VP. B35 mm above HP & 40 mm behind VP. C~40 mm above HP & on VP. D— 35mm below HP & 30 mm in front of VP. Solution : A-1 Quadrant B - II Quadrant C- Las well as II Quadrant Es D-IV Quadrant al 3 1 + i 4 Tt a} | | | : [ot : ae | i 4d Problem 2 Draw the projections of the following Points on the same XY line Keeping convenient distance between each projectors. Name the Quadrants in which they lie. E-30 mm below HP & 25 mm behind VP. F —35 mm below HP & 30 mm in front of VP. ~ G~On HP & 30 mm in front of VP. H- On HP & 35 mm behind VP. Solution w 1 I aE i TT ol | 3 eg | i a] . : | { g x t —t : Y eee i a a Fy 1 | EI Quadrant i | eee F -1V Quadrant Lote +49 G--1.a5 well as 1V Quadrant H--I2s well as III QuadrantProblem 3 Draw and state the quadrants in which the following Points are located. Assume any distances. ‘A- Front view below XY line & Top view above XY line. B — Front and Top views are below XY line. C~Front and top views are above XY line. D— Front view above XY line & top view below XY line. Solution 7 a I ° c i ¢ Xx Y i ob A-ITT Quadrant B- IV Quadrant C- 11 Quadrant D-1 Quadrant a’ 7 d . ed Problem 4 A point 30mm above XY line is the front view of two points A&B .The top view of Ais 40 mm behind VP & The top view of B is:45 mmin front of VP. Draw The projections ofthe points & state the quadrants in which the points are situated, Solution © + ANSWERS: = Aisin iQ BisiniQProblem 5A point ‘A’ is 30 mm in front of VP and 40mm above HP. Another point B is 20 mm behind VP.& 36 mm below HP. The horizontal distance between the points measured parallel to XY line is 60 mm . Draw the three projec tions of the’points. Join their front and top views. Solution xt a a 2 | | A x t t + Y lyf { a, ) 8 60, Ys Problem 6 Draw all the three views of a point P lying 60 mm below HP, 70 mm infront of VP. and'40 mm from the RPP. Also state the quadrant in which it lies, Solution x (HP)VP m 6 RPP YsProblem 7A point P is on HP and 35 mm in front of VP. Another Point Q is on VP and below HP. The line Joining . thei front views makes an angle of 30 deg to XY line , while the line joining thelr top views makes an angle of 45 deg with XY line.Find the distance of the point Q from HP. Solution q i | i | | Point Q is 20.21 mm below HP Problem 8 Two Points R and S are on HP. The point R is 35 mm in front of VP, while Sis 50mm behind VP .The line | joining their top views makes an angle of 40deg with XY. Find the horizontal distance between the two projectors. | Solution s locus of point S 101,66 ANSWER : Distance biw two projectors is 101.66 mm.a) Problem 9A point G is 25 mm below HP & is situated in the third quadrant. Its shortest distance from the intersec- tion of XY and X1Y1 is 45 mm . Draw its projections and find its distance from VP. solution x } | { i Point G is 37,79 mm behind VP 1 Ys * Problem 10 A point Sis in the first quadrant and equidistant of 50 mm from all the three principal planes. Draw the | projections of the point, Draw all the three views ofthe point. Solution 50, iProblem 11 Draw the projections of point G which is in first quadrant such that itis equidistant from HP & VP. The point is 25 mm from RPP. Determine its distances from HP&VP. Solution : te wh, Oxo the dots af ple which J i Phaee? gach Hat it ie equiDinted pom HO,veP ad Re A dictante Joan g | | | | | ' The point is 27.75 mm from VP and HP | Yi Problem 12 Apoint Ris 25 mm above HP & 20 mm in front of VP. Another point S is on HP and 30 mm behind VP. | ‘The distance between their projectors measured parallel to the line of intersection of VP and HP is 50mm. Find the distance between the top views of points R and S. Solution The Distance Between TVs of R and S is 70.7 mm.| | Problem 13 A point M is ch HP-& 30 mmin front of VP, Another point N is 20 mm below HP ald 20 mm in front of VP. The distance between their projectors measured parallel to XY line is 50 mm. Find the distanoe between front views of the points M & N. : Solution x _ Y 2 3 nn PERE as / ‘The Distance Between FVs of M and N is 53.85 m ye Problem 14 A point P is on HP and 30 mm in front of VP. Another point Q is on VP and 40 mm above HP, The distance between their Projectors pall to XY line is 50 mm. Find the distance between their front and top views of the points P and Q. Solution / 50 : q 2 ¢ x A Y 2 a oO 4 A e - 4 ae The Distance Betneen TVS of Pand Qis53.a1 mm The Distance Between FVs of P and Q's 64.03 mn} Problem 15 A point P is 30 mm in front of VP, 40 mm above HP and 50 mm from RPP, Draw its projections. Solution e Left side view _ HP ; r : | °° Se | | Yt Problem 16 The point P is 45 mm above HP, 60 mm behind VP and 30 mm from RPP. Draw the three principles t view of the point. Also state the quadrant in which it lies. Solution x Pa eS I RPP VP(HP) | Y | | I af Point P lies in I Quadrant 8Problem 17 Draw all the three views of a point P lying 60.mm below HP, 70 mm in front of VP and 40 mm from the RPP. Also state the quadrant in which it lies. Solution x Point P lies in TV Quadrant % Problem 18.4 point is 30 mm in front of VP 20 mm above HP & 25 mm in front / behind / from LPP. Draw its Projections and name the side view. Solution x 25 - Right side view at fg iceE eet LPP el | | & w x 4 1 t Y | a 7 al 3) YtProblem'19 A point is 40 mm behind VP, 15 mm‘above HP and.25:mm in front/ behind / from LPP .Draw its projections and name the side view. Solution Xt Left side view VP(HP) a 7%. 45° Yt Problem 20 A point is 30 mm behind. VP, 30 mm above HP and 25'mm in front / behind / from LPP. Draw its projections and name the side view. Solution x Left side view \VP(HP)Problem 21 Apointis lying on HP, 20 mm behind VP & 25 mm behind /in front /from RPP. Draw its projections and name the side view. Solution xX Right side view RPP sw eee a v1 Problem 22 A point is 35 mm below HP, 20 mm behind VP & 25 mm behind infront /from RPP. Draw its projeo- tions and name the side view. Solution Right side view Yt qWProblem 23 Apointis lying on VP, 20 mm below HP & 30 mm behind / infront /from LPP. Draw its projections and xt name the side view. Solution Problem 24 Apoint A is 20 mm above HP & 25 mm in front of VP, Another point B is 25 mm behind VP and 40 mm below HP. Draw their projections when the distance between their projectors parallel to XY line is zero mm, Add the right side view only to point B Solution x b a @ ao a x 9 a 3 a ee Right side view b bProblem 25 Draw the projections of the following Points on the same XY line, keeping convenient distance be- tween each projectors, Name the Quadrants in which they lie. P20 mm above HP & 35 mm in front of VP. Q-30 mm above HP & 40 mm behind VP. R-40 mm above HP & on VP, ‘S— 35 mm below HP & 30 mm in front of VP, Solution bu r | P-1 Quadrant red Q- iI Quadrant Pp a | R - Las well as 11 Quadrant Boi | gz 8 - IV Quadrant | 1? 2 8 x —- 4 7 + —Y 7 | | alo, ff a | : | i 5 P s Problem 26 Draw the projections of the following Points on the same XY line, Keeping convenient distance be- tween each projectors. Name the Quadrants in which they lie. M80 mm below HP & 25 mm behind VP. N.~35 mm below HP & 30 mm in front of VP. P—on HP & 30 mm in front of VP. Q-on HP & 35 mm behind of VP. Solution “ 4 m | g | 8 2 8 Pp x : te y | q 7 8 8 3 | \ a | A-1 Quadrant B- IV Quadrant m P GC - Tas well as IV Quadrant D - Ias well as Ill Quad- rant 13Problem 27 State the quadrants in which the following Points are located. Assume any distances ‘A—Front view below XY & top view above XY line. B—Front and top views are below XY line. C-Front and top views are above XY line, D-Front view above XY & top view below XY line. Solution ¢ A- Ill Quadrant B- IV Quadrant C-U Quadrant a’ D-1 Quadrant 4 d b Problem 28 A point 30 mm above XY line isthe front view of three points P,Q and R. The top view of Ris 40. mm behind VP, the top view of Qiis on XY line and top view of point P is 45 mm in front of VP. Draw the projections of the points & state the quadrants in which the points are situated. Solution i pra)(r) P - 1 Quadrant Q- Las well as If Quadrant R- 1 Quadrant i | 14Problem 29 Apoint’M is 30 mm in front of VP and 20 mm above HP. another point Nin 16 mm behind VP & 25mm ipelow HP. The horizontal distance between the points parallel to XY line is 50 mm . Draw the projections of the points M& N and Join their front and top views. Draw the tight side view for the point N only. Solution \ B \ x - i Y . "Right side view yi Problem 30 The common point 40 mm below XY line represents not oniy the front views of three points A, B and C but also the top view of point C. The top view of point B is lies on XY line and top view of point A lies 50 mm above it. Draw the projections of the points and add the right side view to the point A only. Also state in which quadrants the points le. Solution x A-Ill Quadrant vs B - Ill as well as IV Quadrant C-IV Quadrant 15Problem 31A point Ais on HP and 35 mm in front of VP. Another Point B is on VP and below HP. The line Joining thelr front views makes an angle of 30 deg to XY line while the line joining their top views makes an angle 45 deg with XY line. Find the distance of the point B from HP. Solution i Point B is 20.21 mm below HP Problem 32 Two Points P and Q ate on HP. The point P is 30 mm behind VP, while Qis 50 mm in front of VP .The {ine joining their top views makes an angle of 40deg with XY. Find the horizontal distance between their projectors 1 parallel to XY line. ' Solution | Pp ii Li | | | |) | ‘ | 8 i | ey q | x t Y | : | locus of Q Distance Between Two Projector is 95.34 mmProblem 33 A point Ais 40 mm in front of VP and is situated in the fourth quadrant. its shortest distance from the intersection of XY and X!Y1 is 45 mm . Draw its projections, Also find its distance from HP. xX Solution Point Ais 20.62 mm below HP Ma Problem 34 A point A is 20 mm above HP and in the first quadrant. Its shortest distance from the XY line is 40 mm Draw the projections. Determine its distance from VP, . Solution : x Rs) a o % a 2 roel & vp RPP x - Y HP g ls | Hp Y Distance of A from VP is $4.68 mm 17| | | Problem 35 Draw the projections of the following Points on the same XY line, keeping convenient distance be- tween each projectors and staté the quadrants in which they lie, : P10 mm above HP & 15 mm in front of VP. Q- 15 mm above HP & 25 mm behind VP. |R-25 mm below HP &in VP. = 40 mm above HP & in VP. Solution 40 P-1 Quadrant Q- 11 Quadrant R-II as well as IV Quadrant S -1as woll as II Quadrant x 45 _|10, > et Las Problem 36 Apoint P is 25 mm above HP & 20 mm in front of VP. Another point Q is on HP and 30 mm behind VP. The distance between their projectors measured parallel to the line of intersection of VP and HP is 50mm. Find the distance between the top views of points P and Q. Solution Distance Between TVs of P and Q is 70.7 mm 18- Problem 37 Apoint Ais on HP & 80 mm in rit of VP. Another point B is 20 mm below HP and 20 mm in front of VP. The distance between their projectors measured parallel to XY line is 50 mm. Find the distance between the front views of the points A & B. Solution 50 Jy / b' (b) a é oN Distance Between FVs of A and B is 53.85 mm Problem 38 A paint P is on HP ‘and 30 rim infront of VP. Another Point Q is on VP and 40 mm above HP. The distance between their projectors parallel to XY line is 50mm. Find the distance between thelr front and top views of the points P and Q. | Solution 50 a | p\ Distance Between TVs of P and Q is 68.31 mm Distance Between FVs of P and Q is 64.03 mmProblem 39 Draw the projections of a point A lying 30 mm above HP and in first quadrant, if its shortest distance from the line of intersection of HP and VP is 50 mm. Also find the distance of the point from VP. Solution x 7 3 ve : x y = 5 ‘1 Distance of A from VP is 40 mm | Problem 40 Draw the projections of the following points on the same reference XY line and state the quadrants in which they lie. E~36 mm above HP & on VP F—30 mm below HP & on VP G-OnHP & 25 mm behind VP H—On HP &30.mm in front of VP { Solution 1 | — i 8 g 8 f ou a x te + i__# — Y Z| a | : * | fe of Lh E - Las well as II Quadrant F - Ill as well as 1V Quadrant G- Il as well as III Quadrant H - 1 as well as IV Quadrant 20Problem 41 A point 20 mm below the reférence XV line isthe top view of three points P, @.& R. P is 20 mm below HP, @ is 35.mm above HP and Ris on HP. Draw the projections ofthe three polnts and state their positions. & ‘quadrants in which they are situated. Solution 7 P - 20 mm below HP and 20 mm infront of VP, V Quadrant Q- 35 mm below HP and 20 mm infront of VP, | Quadrant R- on HP and 20 mm infront of VP, laswell as IV Quadrant (a(n) P Problem 42 A point is 30 mm in front of VP, 20 mm above HP & 25 mm in front / behind / from LPP. Draw its Projections and name the side view. Solution x 25 : r— a a" ——_—- —_ Right side view ol 8 LPP i x r Y % HP 8 a v1 24i | | Problem 43 A point is 40 mm behind VP, 20 mm above HP and 80 mm in front / behind / from LPP.Draw its, projections and name the side view. Solution Left side view 40, VP(HP) YA Problem 44 A point is 30 mm behind VP, 30 mm above HP, and 25 mm in front / behind / from RPP. Draw its projections and name the side views. Solution xi 25 e© 30 VP(HP) ee ‘1 22Problem 45 Apointis lying on VP, 10mm below HP & 30 mm behind /in front / from LPP. Draw its projections and name the side view. 5 Solution x yt Choice Choice eating the point is in ill Quadrant, itis left side view : Treating the point is in IV Quadrant, itis right side view Problem 46 Apointis lying on HP, 20 mm behind VP & 35 mm behind /in front from RPP, Draw its projections and name the side view. Solution xX 35. Right side view 20 VP(HP) ae rs Yt 23| ' | | | Problem 47 A point is 35 mm below HP, projections and name the side view. Solution 15 mm behind VP & 25 mm behind / infront / ftom RPP. Draw is 45 HP. VP. 35. Right side view Y1 Problem 48 Apoint Pis 15 mm above HP & 25 mm in front of VP. below HP. Draw their projections when the distance between their right side view only to point Q. Solution Another point @ is 25 mm behind VP and 40 mm Projectors parallel to XY line is zero mm. Add the xX Right side view ¢ ¢ 24Problem 49 Draw the projections of the following Points on the same XY line, keeping convenient distance be- tween each projectors. Also state the quadrant in which they lie. P~25 mm above HP & 36 mm in front of VP. Q~30 mm above HP & 40 mm behind VP. R-40 mm above HP & on VP. $35 mm below HP & 30 mm in front of VP. Solution ’ 7 rt 8 x \ | 4 ib; P- 1 Quadrant Q- II Quadrant R - Las well as Ii Quadrant $+ TV Quadrant ————y Problem 50 Draw the projections of the following Points on the same XY line, Keeping convenient distance be- tween the projectors. Also state the quadrants in which they lie . ‘A~ 30 mm below HP & 25 mi behind VP. B~35 mm below HP & 30 mm in front of VP. C~on HP & 30 mm in front of VP. D—on HP’& 35 mm behind of VP. Solution cl eH —- | 3 al x { 7 eaag +5 y | 2 io a 2 8 b 4 7 oe : ity A- IM Quadrant B - IV Quadrant G- Las well as IV Quadrant D- I as well as II Quad- rant 25| CHAPTER 2 PROJECTIONS OF LINES: Problem 1/Aline AB 80 mm long has its end A 20 mm above the HP and 30 mm Infront of VP. Itis inclined at 30° to HP and 45° to VP. Draw the projections of the line and find apparent lengths and apparent inclinations, Solution 20 ANSWERS : Problem 2 Aline AB 80 mm long is inclined to HP at 30° and inclined to VP at 45°. Draw front and top views of line and determine their lengths. Also measure the perpendicular distance of end B from both HP and VP. Solution ANSWERS : 27Problem 3 ‘line AB has its.end A 20 mm above the HP and 30 mm infront ofthe VP. The other end B is 60 nm above the HP. The distance between end projectors s 70 mm. draw its projections. Determine the true length and apparentinclinations, Solution 45 | j ANSWERS: | O=30° A 7 a EE aun 1! i 7 Problem 4 Aine AB has its end A20 mm above the HP and 15 mm infront of the VP. The other end B is 60 mm above the HP. The distance between end projectors is 70 mm. draw its projections. Determine the apparent lengths and true inclinations. SolutionProblem 5.The top view PQ of a straight ine is 70 mm and makes an angle of 60° with XY line. The end Q is 10mm infront of VP and 30 mm above the HP. The differente between the distances of P and Q above the HP is 45 mm. draw the projections. Determine its true length and true inclinations with HP and VP. Solution ANSWERS ; Problem 6 Aline P@.85 mm long hasits end P.10 mm above the HP and 1 mm introntof the VP. The top view and front view of line PQ are:75.mm and 80.mm respectively: Draw its projections. Also determine the true and apparent inclinations of the line. . Solution ANSWERS : 29Problem 7 Aline has its end A 10 mm above HP and 15 mm infront of VP. The end B is 55 mm above HP and line is inclined at 30° to HP and 38" to VP. The distance between the end projectors is 50 mm. draw the projections of the line. Determine the true length of the line and its inclination with VP. Solution e - ve g x ‘HP re 7 ANSWERS ; = 42" / Baas i / TL=80 b be Problem 8 The top view of a line 75 mm long measures 50 mm. the end Pis 30 mm infront of VP and 16 mmabove HP. The end Q is 15 mm infront of VP and above HP. Draw the projections of the line and find its true inclinations with HP and VP. ‘Solution ga \ L=71 ANSWERS O=49" g=1? o=50° B=17 30| t i i Problem 9 Aline AB 60 mm long has one of its extremities 20 mm infornt of VP and 15 mm above HP. The line is inclined at 25° to HP and 40° to VP, Draw its top and front views. Solution Problem 10 Aline AB measuring 70 mm has its end A 15 infront of VP and 20 mm above HP € \ yy 2 \ (ZR | Ne | i vem | —H + wal] 8 tt. - - a } | IN al i TNOY | | \ 1 | / | ——-—- ANSWERS : and the other end B is 60 infront of VP and 50 mi above HP, Draw the projections of the line and find the inclinations, of the line with both the reference planes of projection. Solution HP 3| Problem 14 The front view of a 90 mm iong line which is inclined at 45° to the XY line, measures 65 mm. End is 15 mm above the XY line and is in VP. Draw. the projections of the line and find is inclinations with HP and VP. _ Solution . ve ANSWERS : b=49 a= 76° B=76 cee eee Problem 12 The distance between the end projectors through the end points of a line AB is 60 mm. The end Ais 10 mmvabove HP and 15 mm infront of VP. The end B is 35 mm infront of VP. The line AB appears 70 mm jong in the front== view, Complete the projections. Find the true length of the line and its inclinations with HP and VP. SolutionProblem 13 The distance between the'end Projectors through the end points of a line AB is 40 mm. The: end Ais 20 mm above HP and 15 mm in front VP. The end B is 45 mm infront of VP. The line AB ‘appears 50-mm tong in the front. view. Complete the projections. Find the true length of the line and its inclinations with HP. and VP. Solution : | \ \ i 6 \ tad \ | ah 4 ele oF : 8 ; VP X- } L Y HP i Ep | i S } : eo Eo ANSWERS : . ( ‘ O=42 Ne bP Problem 14 The paint B of a line AB is on the horizontal plane, the top view of the line makes an angle of 30°with XY line, being 80 mi. The point A is on the vertical plane and 60 mm above the horizontal plane. Draw the top and {front views of the line and obtain the true length of the line. Also find the inclinations ofthe line with the two planes, Solution 50 ve 7 x Y HP ANSWERS : O=25° o=32 i =. TL=95Problem 15 Draw the projections of a straight line AB, 100.mm long, inclined at 45° to HP.and 90° to VP. The end. Ais in HP and the end Bis in VP. Find the shortest distance between the straight line AB and the line of intersection of planes of projection. Solution Loc of ANSWER : sD=41 ° i Problem 16 Aline AB 100 mm longis inclined to HP at 46° and inclined to VP at 30°, Draw front and top views of line and determine their lengths. Also determine the perpendicular distance of end Q from both HP and VP. “ SolutionProblem 17 The top view of a 75 mm long line AB measures 65 mm, while the front view is 50 mm. Its one end A isin the H.P and 12 mm in front of the V.P. Draw the projections of AB and determine its inclinations with the H.P. and the VP. Solution ANSWERS : 6=30 o=a = 48° B= 60° Problem 18 Aline AB, 65 mm long, has its end A20 mm above the H.P and 25 mm in front of the V.P The end B is 40 mm above the H.P, and 65 mm in front of the V.P. Draw. the projections of AB and show its inclinations with the H.P.and the V.P, Solution ANSWERS : 8-10 =38" 35Problem 19 Astraight ine PQ, 65 mm long, is inclined at 45° to HP and 30° VP. The point P is 70 mm from both the reference planes and the point Q is towards the reference planes, Draw the projections: Solution ANSWERS : = 55° B=ase Problem 20 A point Pis 40 mm above HP and 20 mm infront of VP another point Q is 20 mm above HP and 50mm, i infront of VP. The top view of line PQ is inclined at 30° to XY. Draw the projections. I Solution Pp : en VP. HP. | 20 ANSWERS : O=18° o=28" TL=63 36| | i Problem 21 The top view of a ine PQ is 70 mm and front view is 60 mm long. The end Qis nearer to both HP and: VP than the end P and is 15 above HP arid 20 mm infront of VP. Draw the projections of the line if the distance between projectors is 50 mm, Solution : 7 ANSWERS : 6=25° o=408 Problem 22 Aline AB 100 mm long measures 80 mm in front view and 70 mm in top view the mid point M of the line is 40 mm from both HP and VP. Draw its projections. Find its inclinations. Solution 37om Problem 23 Aline has its end A 15 mm above HP and 10 mm infront of VP. The end B is 55mm above HP and the line is inclined at 30° to HP. The distance between the end projectors is 50 mm..draw the projections of the line and determine the true length of the line and its inclinations with VP. Solution Problem 24 Aline MN 90 mm long has a point P on it which divides the line in the ration 2:1, i.e. MP: PN = 2:1. this point P is 50 mm above HP and 60 mm in front of VP. The line is inclined at 35° to HP and 40° to VP. Draw the projection of the line. Find the distance between end projector and the position of the ends of the line with HP and VP. Solution * 38Problem 25 Astraight line PQ inclined at. 40° to VP has) ‘Pq = 60 mm and p’q’ = 50 mm. The end Pis bath in HP and VP, and 40 mm to the right of lft profile plane 2) Drawthe projections of the straight line PQ. b) Find he true length and true inclination with HP. ©) / Draw the profile view of the straight line. 4d), Find the position of the end Q with HP and VP. Solution x | Hl i i | ica ve 3 | MEI x 1 a y HP ln . 7 fd ANSWERS: ~/ ee O=19 | 8° L & G 3 snabsaast : : Ht B=40 ; ae TL=59 a L=39 M=20 } : Yi Problem 26 Aline has one énd 30 mm in front of VP and 15 mm above HP and the other end is 16 mm in front of VP and is above HP. Length of the line is 60 mm. Top view of the line is 40 mm fong. Draw the two views of the line afd obtain the inclination of the line with HP and VP. Solution ae be Loci of B ANSWERS : O24 ox" 39Problem 27 The top view of line PQ 75 mm long measures 50 mm. The end Piss 30 mm in front of VP and16 mim | above HP. The end Q is 15 mm in front of VP and above HP. Draw the Projections of the line and find its true inclinations with HP and VP. Find the length of front view and distance between the end Projectors. a Solution oe ae \ \ t 0 \ if : Pe eee eee eee 2 ee eer vw ~ + | x : Y } HP 9) | 8 ie Problem 28 Astraight line AB measuring 80 mm long has the end Ain the HP and 25 mm in front of the VP. Its mid point M is 25 mm above the HP and 40 mm in front of the VP. Draw the projections of the line and determine the inclination of the fine with HP and VP. Solution 40Prpblem 29 The front view of the line PQ 80 mm long measures 50 mim and itis inclined to XY (reference lina) at ‘50. One end of the line P is 20 mm above the HP and 25 mm in front.of the VP. Draw the front view and top view of the line and find the inclinations of the line with HP and VP. Solution cod \o N L-N ae ANSWERS : 0-9 a5" Bee? “qm Problem 30 Drawthe projections of a line AB 100 mm long inclined at 459 to VP and 300 to HP. One end of the line 's 20 mm above the HP and in the VP. Also determine the apparent length and inclinations, Solution 4/ | Problem 31 Draw the projections ofa line PQ and find its true length and inclinations when the line is inclined at 300 to the HP and 45° to the VP. The line is having one of its ends 15 mm above HP and 20 mm in front of VP. The distance between the end projectors on the XY ine is 60 mm, Solution “ AS en Steps, Besa TACO Problem 32 The top view ab of a straight line AB is 60 mm long and makes an angle of 20° with the XY. ling. The end Ais in VP-and 30 mm above HP. The end Bis 65mm above HP. Draw the projections of the line AB and determine 4) length of the front view ii its true length and true inclinations with the reference planes. Solution ANSWERS : 6=0 42Problem 33 A tine AB 65 mm long, has its end A 25 mm abo mm above HP and'50 mm in front of VP. Draw the projections / Solution ve HP and 80 mm in front of VP. ‘and determine its inclinations. i | its top view measuring 60 mm, is inclined at 500 to XY, Draw the pr | inclination with VP, vo | Solution \ ANSWERS : 9=36° TL=78 aaProblem 35 The top view of the line AB 80 mm long, measures 65 mm. The mid point of the line is 60 mm in front of VP.and 70 mm abéve HP. The point Ais in the VP. Draw its projections and find its inclinations. Solution | | | | 40 < 30 ANSWERS : Problem 36 Astraight line PQ is inclined at 45° to HP and 30° to VP. The point Ps The length ofthe straight line is 65 mm. draw the projections ofthe straight line AB, Solution in HP and the point Qis in VP. ‘ANSWERS : 6=36 o=49 44Problem 37,Draw the projactions of a line AB 90 mm long and find its true-and apparent inclinations with HP and VP, when its end Ais on HP and 20 mm in front of VP. Its midpoint Mis 20 mm above the HP and 40 mm in front of the ve. Solution ¥ “0 pe oa? Problem 38 A line PQis inclined to both HP and VP by 30° and 45°respectively. one of its ends P is at a distance of 10 mm from HP and 15 mm from VP. The distance between the end projectors is 45 mm. Draw the top, front and right side views of the line. Determine the true length of the line and the distances of the end Q from VP and HP. Solution ANSWERS : 1 =46° oo Bass 45Problem 39 Two lines AB and AC make an angle of 120" between them in their front view and top view. AB is parallel to both the HP and the VP. Determine the real angle between AB and AC. Solution . | x | HP | bf ANSWER ; @= 112 ° Problem 40 The elevation of a line AB 90 mm fong, is inclined at 30° to HP and measures 70 mm. The end A is 20 mm above HP and is in VP. Draw the projections of the line and find its inclination with VP. Solution bo be ANSWERS : G= 23° o=39" Baas 48Problem 41 Aline PQ measures 80 mm in length. The point P is above HP and infront of VP by 20 mm and 30 mm respectively. The distance between the end projectors is 50 mm, the line is inclined to VP by 30°. Draw the projections of the line and specify its true inclination with HP. Solution j ANSWERS ; Problem 42 The top view ofa line PQ 75 mm long measures 50 mm and the front view measures 60 mm. The end P is 30 mm above HP and 15 mm infont of VP . Draw the projections of the line and find its true inclinations with HP and VP. Find length of front view and distance between the end projectors. Solution ANSWERS ; O=4s" o=37 D=2 47 | | | | | |Problem 43 Astraight line AB measuring 80 mm long has the end Ain the HP and 25 mm infront of the VP. Its mid point M is 25 mm above HP and 40 mm infront of the VP. Draw the views of the line and determine the inclination of the line with HP and VP and also find distance between end projectors. Solution VP. 7 XHP Y | ANSWERS : | O=3" | = i D=55 Problem 44 The endAof a line AB is in HP and 25mm in front of VP. The end B is 25 mm infront of VPrand 50mm above HP. The distance between the end projectors when measured parallel to the line of intersection of HP.&.VP.is 65mm. Draw the projections of the fine AB and determine its true length and true inclinations with HP & VP. | Solution ANSWERS : 0=36° =I? | | | | TL=86 48Problem 45 Aine has its end A, 15mm from HP & 10 mm from VP. The end B is 85mm from HP and the line is inclined at 30° to HP. The distance between the end projectors is 50mm. Draw the projections of the line. Determine the true length of the line and its inclination with VP. Solution ANSWERS : 6 = 28° Problem 46 The end Acta line AB is in HP and 25mm in front of VP. The end Bis 10 mm in front of VP and Somm. above HP. The distance between the end projectors when measured parallel to the line of intersection of HP & VP is ‘80 mm. Draw the projections of the line AB and determine its true length and true inclinations with HP & VP, e Solution u bbe a 4 - A Z f | \ | \ 8 \ ° : | ve : | x be ZI 4 Y He FRocLEecucececer rere ereeceecaeeeeere hy al | Z 3 eee S| 49| i | | | | | i Problem 47 Astraight line PQ 80 mm long appears to a length of 50 mm and inclined at 300 to xy line ints top view.” Draw its projections when its end point P is 15 mm above HP and 60 mm infront VP. Point Q is nearer to VP than P. Solution ANSWERS: O=18 a2 Beast Problem 48 The top view of a line AB, 80mm long measures 65mm and the length of the front view is SOmm. The x Ys ‘end Ais on HP and 15mm infront of VP. Draw the projections Solution SERS PoProblem 49 Draw the projections ofa line PQ and find its apparent lengths, true length and tre inclination with HP \when the line PQ has its end P 25 mm above HP and 20 mm infront of VP. The cistance between the end projactorsot the line when measured parallel {othe line of intersection of the HP and VP is 60 mm. The end Q is 50mm above the HP and the line is inclined at 30° to the VP. Solution ve 25 G2 50 HP 20 q ANSWER Hy =65 PQ =1077 \/ a =B° / 6 332° g f PQ=p'g'=pq=75.06 & 7 51Problem 80 Find the true length and true inclination ofa line AB with HP having one ofits ends 20 mm infront of VP ‘and 30 mm above the HP. The line is inclined at 40" to VP and the right side view ofthe line is 60 mm long} and inclined ‘at 60" to the X11 line, Draw all the three views of the line. Solution \ i ® * ¥ t Pa ’ % sae - | —+— a6 Bs € « z a= 52 bianca nena iCHAPTER 3 PROJECTIONS OF PLANE SURFACES * Problem 1 An equilateral trianguiar lamina of 25mm side lies with one of its edges on HP such that the surface of the lamina is inclined to HP at 60°. The edge on which it rests is inclined to VP at 60°. Draw the projections. Solution ve bia) cl HP i Problem 2 An equilateral triangular lamia of 25mm side lies on one of its sides on HP. The lamina makes 45° with * HP and one of its medians is inclined at 40° to VP. Draw its projections. Solution Cc om smh Ng x ‘(a’) c bia’) i a b' Y HP aI ON 53¥ Problem 3 Atriangular lamina of 25mm sid the comer on which it rests is inclined at 30° Solution — es fests on one of comers on VP such that the median passing through ‘to HP and 45° to VP. Draw its projections. \ , Be 2 \ Problem 4 A triangular plane figure of sides 25m the lamina makes an angle of 60° with HP. Ifthe si ‘of 30° with VP, draw the top and front views in thi Solution im is resting on HP with one of its corners, such that the surface of ‘de opposite to the comer on which the lamina rests makes an angle 's position, ve) e | at bie) ae vp x Y al HP | b Problem 5 Atriangular plane lamina of sides 25mmis, esting on HP with one of its comers touching it, such that the side opposite tothe comer on which t rests is 15mm above HP and makes an angle of 30° with VP. Draw the top and | {font views inthis position. Also determine the incinaton ofthe lamina to the reference plane. Solution | | | 54+ Problem 6 A30"-60° setsquare of 60mm longest side is so kept such thatthe longest side is in HP, making an angle of 30° with VP. The set square itself is inclined at 45° to HP. Draw the projections of the setsquare. Solution cc c bay ry i bay og ” coh vey = ! 7 3 1] HP al al c cae 2 3 Ne by , l/ AN. ic | SO | 4 p we «Problem 7 An isosceles triangular plate of negligible thickness has base 25mm long and altitude 35mm. Itis so Placed on HP such that in the front view itis seen as an equiteral triangle of 25mm sides with the side thats parallel to VP iginclined at 45°to HP. Draw its top and front views. Also determine the inclination of the plate with the reference plane, : Solution 35 i z , bt wo /. | 8 e fc | ve 1 ye ‘ || HP c a b b b 55* problem 8 Asquare lamina of 40mm side rests on one of its sides on HP. The lamina makes 30° to HP andthe side ‘on which it rests makes 45° to VP. Draw its projections. 7 i Solution é (e)b" b e ve a @) wer ae) Se a e | RP r 5 . | le ® | a Ae q ‘ | : : 4 i q y I G / | : I 1a b al ° | 7 a % i | vy b i | jorren V4 Problem 9 Asquare plate of -abmm sides rests on HP such that one of the diagonals is inclined at0%o HP and 46° to VP. Draw its projections. Solution =” vp. HP 56foblém 10 A: ABCD of 40mm side rasts-on como ‘such that the diagonal AC appears to be at 45%o 3 and! gee See aereeee 4 VP. The two sides | ‘containing the comer C make equal inclinations with HP. The surface of the lamina. makes It 80° with HP. Draw its top and front views. i Solution i ; | | é e | 7 ¢ i \ i | Y | 4 i N ! 1 i i e i i | N | ¢ | | ' wet te Loma 7 y VProblem 11 The top view of a square lamia of side 30mmis a. ‘rectangle of sides 30mm x 20mm with the longer side | ‘sof the rectangle being parallel to both HP and VP. Draw the top and front views of the ‘square lamina. What is the | 4 inclination of the surface of the lamina with HP:and VP? | | Solution ; x siden - RPP ww mm | sv | te) Eee geet ee wey Y tee | | ve ad) we a@/ ® a a 5 a

a b |_20 | : ; * Lvs roblem 13 A rectangular lamina of 35mm x 20mm rests on HP on one of ts shoiter edges. The lamina is rotated ‘about the edge on which it rests til i appears as a square in the top view. The edge on which the lamina rests being parallel to both HP and VP. Draw its projections and find its inclinations to HP and VP. Solution x RPP Lsv 4 | ve at 7 Ne) bre) — y HP t . B o , EES a > 58wgfebiem 14 Arectangular lamina of 35mm x 20mm, testoan HP on one of its shorter edges. The lamina is rotated ut the edge on which itrests tl itappears as a squere in the top view. The edge on which the lamina rests is inclined ‘30° to VP. Draw its projections and find its inclination to HP. Solution \ c) > c } &, : VP ata) bY) _ ad’) i / x y HP ; 7 ea 1 gl Z _ 36 2 belo 15 Arectangular lamina of sides 20mm x 26mm has an edge in HP and adjoining edge in VP,stited such I that the front view appears as a rectangle of 20mm x 15mm, The edge, which isin VP, is 20mm from the right profile * plane. (a) Draw the top view, front view and the eft profits view in this postion, (b) Find is inclinations with the corresponding principal planes. Solution 4 i x : we RPP 5 yh? Lsv ' 8 4 ra Ikke. + a & VP. " a r a o " Rp ‘dy 5 at 3 ; x : } Y Y \ i, i % y 30 Y 59eek, (of Probiost 46 The front view of a rectangular lamina of sides GOmm x 20mm is square of 20mm sides. Draw the projections and determine the inclinations ofthe surface ofthe lamina with HP and VP, Solution Y OK roblem 17 Amitror 3omm x 40mm is Ne inclined the wall such thats font view is @ square of 20mm side. The © onger sides ofthe mirtor appear perpendicuiar to both HP and VP. Find the inlnation ofthe miror wit the wall. tion N in Solu \ % Rep 20 sv 4 ie ae) 5 r fey | ae | § vl e lw | ol by Xe ap a9) oy, a 5 %lem 18 A rectangular plate of nogigible thickness of size S5x20mmhas one ofits shorter edges th VP with that lined at 40° to HP. Draw the top view fits front view is a square of side 20mm, os i y Solution ey 20 35 020, 7 ef TST le gq ? d bt a ; a jb i 4 i} it : j $/ oP & a HP dia) eb) a" /j | He Problem 19 A pentagonal lamina of edges 251mm is resting on HP with one ofits sides such thatthe surface makes A" an angle of 60° with HP. The edge on which it ests is inclined at 45° to VP. Draw its projections, Solution : c ce é ale) ba’) oc vp HP. 6tProblem 20 Apentagonal lamina of edges 25mmis resting on HP with one of its comers such that the plane surface rmiakes'an angle of 60° with HP. The two of the edges containing the corner on which the lamia rests make equal inclinations with HP, When the edge opposite to this corner make an angle of 45° with VP and nearer to the observer, draw the top and front views of the plane lamina in this position. Solution vp HP // Problem 21 A peniagonal lamina of ‘edges 25mm is resting on HP with one of its comers such that the edge ‘opposite to this corner is 20mm above HP & makes an angle of 45° with VP. Draw the top and front views of the plane v lamina in this position, Determine the inclination of the lamina with HP. Solution ve a be) e(d)Problem 22 Apentagonal lamina of sides 26mm is resting on one ofits edges on HP with the comer opposite to that edge touching VP. This edge is parallel to VP and the comer, which touches VP, is ata height f 1mm above HP. Draw {the projections ofthe lamina and determine the inclinations of the lamina with HP and VP and the distance at which the parallel edge lies from VP. Solution ; # Problem 23 Apentagona! amit having edges 251mm is placed on one ofits corners on HP such that the petpen- dicular bisector of the edge passing through the comer on which the lamina rests is incfined at 30° to HP and 45° VP. “Draw the top and front views ofthe lamina. Solution x eee ea) we | R +t | | Im a © 6 , Problem 24 A pentagonal lamina of sides 25mm is having @ side both on HP and VP. The comer opposite to the ‘side on which it rests is 15mm above HP. Draw the top and front views of the lamina. Solution +H 63~ "Problem 25 A pentagonal lamina of sides 25mm Is having a side both on HP and VP: The surface of the lamina is i inclined at an angle of 60° with HP. Draw the top and front views ofthe lamina. Solution i { ah ‘ ae. ‘ ‘ ae) bie) Problem 26 A regular pentagonal lamina of 25mm side is resting on orte of its comers. on HP while the: side ‘opposite to this comer touches VP. Ifthe lamina makes an angle of 60° with HP and 30° with VP, draw the projections 6 ofthe lamina. Solution a be) vey a le HP| | i | | x Problem 27 A pentagonal lamina having edges 25mm is placed on one of its comers on HP such that the surface makes an angle 30° with HP and perpendicular bisector of the edge passing through the comer on which the lamina rests appears fo be inclined at 30°to VP. Draw the top and front views of the lamina. SOHN 6 Syinattion ¢ (a) = _ oo? g vp a ep cd) ra x Y HP e | d 4 jm anne an a) fe m 1} 6 >—~_ i a € \ ae Problem 28 A regular pentagonal lamina of 25mm side is resting on one of its sides on HP while the comer opposite to this sids touches VP. Ifthe lamina makes ah angle of 60° with HP and: SO-mile7P"draw the projections of the lamina. Solution 2GAD8 1S Sane ype of pH. oe ‘ ¢ : ( j bid) \ / ; e P Nes ae ye) / ‘i \e ale) by cate) / Y va vey | a HP d d b | e e a _|\, ve a 65‘ roblem 29 A pentagonal lamina of edges 25mm is resting on VP with one of its sides such that the surface makes, an angle of 60° with VP. The edge on which it rests is inclined at 45° to HP. Draw its projections. ae 7 qd oor 4 oe e.. : | Di c bt 7 , a | | Hee : vp T up Y | | | ; & bid) a HEE ) wy vf roblem 30 A pentagonal lamina having edges 25mm is placed on one of its comers on VP such that the surface makes an angle 30° with VP and perpendicular bisector of the edge passing through the comer on which the lamina rests appears to be inclined at 30° to HP. Draw the top and front views of the lamina, Soliton 66i eer i yo Selo R04 Laan fp eae wD Cah \ Ny cadpnh slid Problem 31 Apentagonal lamina having edges 26mm is placed on one ofits comers on VP such that the suiface makes an angle 30° with VP and perpendicular bisector of the edge passing through the corner on which the lamina rests is inclined at 45° to HP. Draw the top and front views of the lamina. Solution x d(e) rr, Problem 32 A'hexagonal lamina of 80mm sides rests on HP with one of its comers touching VP and surface inclined at 45° to it, One of its edges is Inclined to HP at 30°, Draw the front and top views of the lamina in its final r position. Solution» — , LM I Pas cgi oh 3 i a vf) | | / | | —)—____x or of. wahination — WP & —nichuviltiow ~ ue 67Problem 33 Draw the top and front views of a hexagonal lamina of 30mm sides having two of its edges-parallel to ‘both and hora planes and one of its edges is 10mm from each of the planes of projection. The surface ined at 7 | ofthe hina is inclined at an angle of 60° to the HP. | Solution ; | ae e a 3/ Ay | 7 | | x / ey i —+ F i) af) (eb i’) et aif), v t j 7 f ve 2 i | Xp 1 T aT 7 | A | al - Poet a 6 . Cn Y SS ce d 7 | * i Problem 34 Aregular hexagonal lamina of sides 30mm is lying in such a way that one of its sides touches both ‘the reference planes. If the lamina makes 60° with HP, draw the projections of the lamina. Solution * sgh Ye| a Ce me Problem 35 A regular hexagonal lamina of side 30mm is lying in such a way that one of its sides touches both the reference planes. If the side opposite to the side on which It rests is 46mm above HP, draw the projections of the Ltamina. Solution x # er fre") ff ¢ \ Ste) at ol a fe ‘| ve | we efor | ° % aa 09 alo Sit x BR Ss, oy 81Problem 6 Apeniagonal prism 25 mm sides of base and 60 mm axis length rests on HP.on one of its edges of the base. Draw the projections of the prism when the axis is inclined to HP at 40® and VP at 30°. f Solution 82 t| 4 Problem 7 Apentagonal prism 25 mm sides of base and 50 mm axis lengih rests on HPon one ofits d seers ot base such that the two base edges containing the comer.on which it rests make ‘equal inciinations with HP. Drawing Peele prism when the axis of the prism is inclined to HP at 40° and appears to be ftined fo VP at 452, ‘olution i cae . - i} i | 2 | » on 3 52) 2 1 0 5 Hee = q's g Ve a I] | |\. ie i ri 5 4 ‘| q bh ttt at Vi 3 Gs g | > 3 is a FI : is g VE 2 a s}->——- J 8 5 - zt i | 5 . BEE iar Se sie ea 83| Problem 8 Apentagonal prism 25 mm sides of base and 50 mm axis length rests on HP on one ofits comers of the | base such that the two base edges containing the comer on which it rests make equal inclinations with HP. Draw the projections ofthe prism when the axis ofthe prism is inclined to HP at 40® and to VP at 30°. Solution & | © = | 1 | [ | | % = + <3) | 2. ! 2 3 ‘ X x : \ ALE ty z 3 | \ \ . | i S | : 3 > | | t | : | ‘ le | | i % Ss ; 3 3 a | 3] S |= | —--| Ss : 2 ——r o a ” S| i | = S| = gz eo 4 a w ala SE a aie ead St *Problem 9 A hexagonal prism26 rim sidés of base and 50 mm axis length rests on HP on one ofits edges, Drawthe projections of the prism when the axis is inclined to HP at 45° and appears to be inclined to VP 40°. Solution 7m lo a N a z ; -R 3} 6 | | ‘ wy dg bes c § sf eT 5 L Bek g <* a e 3 ae y os 85 eld] xProblem 10 A hexagonal prism 25 mm sides of base and 50 mm axis length rests on HP on one of its edges of the base, Draw te projections ofthe prism whe the seis ned! to HP et dePand VP.ot 30g Solution Ee = le E zg = Z| | — 3 3 3 a 2 - fa 2 3 fs Pouseceereretee) ale Es xe 86Problem 11 Ahexagonal prism 25 mm sides of base and 50 mm axis length rests on HP on one ofits comets of fe ‘base such that the two base edges containing the corner on which it rests make equal inclinations with HP. Draw fhe Projections ofthe prism when the axis of the prism is inclined to HP at 40® and appears to be inclined to VP at 45%, Solution “19 6 > x 2 | ls ig wy 3, 3 a. L ol - \ \I ~E 6 oa a s 6 g = | | je z| s| & ie = 3 Le S|. Hts Z al 3 iS a 2 z| =} o z g 2 < 3 . a 3 08 87' Problem 12 Ahexagonal prism 25 mm sides of base and 50 mm axis length rests on HP.on one ofits corners of the base such that the two base edges containing the comer on which it rests make equa inclinations with HP. Draw the projections ofthe prem when the axis ofthe prism is inclined toHP at 40%andto VP at308, g ” Solution ¢ el =| gl is Ee 3 & ‘B 5 | 5L—- - 1g 5 a t + S| cs zg 3 o 8 2 < =z 3 88Probion( rd. ‘square prism 35 mm sides of base and 60 mm axis lengths suspended freely from a comer ofits base. Draw the projactions ofthe prism when the axis appears to bo inclined to VP at 45°. Solution ono fo] b, Tel\, aia] bib] ole did] \ bidet olProblem 14 Apentagonal prism 25 mm sides of base and 50mm avis length is suspended freely from a comer of its base. Draw the projections of the prism when the axis appears to be inclined to VP at 45%. Solution a 90i: Problem 15 Ahexagonal pism 25 mm sides of dase and60'mmn axis length is suspended freely roma comer ofits £280. Draw the projections ofthe prism when the axis appears to be iplnedto VP et se Solution oe i i | bifl cle} 5 te. 91Problem 16A square pyramid 25 mm sides of base and 65 mm axis length resis on HR on one ofits edges of the base which is inclined to VP at 30°. Draw the projections of the pyramid when the axis is inclinéd to HP at 45%, Solution nop 92‘base such that the two base edges containing the comer on which itrasts make equal inclinations with HP. Draw the brojections of the pyramid when the axis ofthe pyramid fs inclined to HP at 40e ™ ‘and appears to be inclined to VP at 459, Solution >Problem 18 A square pyramid 35 mm sides of base and 60 mm axis length rests on HP on one of its corners of the base such that thé two base edges containing the comer on which it rests make equal inclinations with HP. Draw the Brojections ofthe pyramid when the axis ofthe pyramids inclined to HP at 40® and to VP at 308, Solution : t Is . 2 2 a 1 a a o / oy i : KY | ~ 09 ‘ & | I | xProblem 19 A square pyramid 35 mm sides of base and 60 mm axis length rests on HP on one of its edges of the base. Draw the projections of the pyramid when the axis is inclined to HP at 45° and VP at 30°, ¢ Solution 95Problem 20 Apentagonal pyramid 25 mm sides of base and 60 mm axis length rests on HP on one ofits edges of the base which is inclined to VP at 30°. Draw the projections of the pyramid when the avis is inclined to HP at 40%. | Solution no 96Problem 21,Apentagonal pyramid 25 mm sides of base and 50 mm axis length rests on HP on one of its edges of the base. Draw the projections of the pyramid when the axis is inclined to HP at 45° and VP at 0°. 2 Solution 97Problem 20 A pentagonal pyramid 25 mm sides of base and 60 mm axis length rests on HP-on one ofits edges of the base which is inclined to VP at 30°, Draw the projections of the pyramid when the axis is inclined to HP at 40%, Solution _}o le oe - - s oo a 2 ‘ a D 3 3 ‘ 98 ala S\r xProblem 22 Apentagonal pyramid 26 mm sides of base and 60 mm axis length rests on HP on one ofits comers of | the base such that the two base edges containing the corner on which it rests make equal inclinations with HP. Draw | the projections of the pyramid when the axis of the pyramid is inclined to HP at 40° and appears to be Inclined to VP at ye Solution ofo] rd 98Problem 23 Apentagonal pyramid 25 mm sides of base and 50 mm axis length rests on HP on one ofits comers of the base such that the two base edges containing the comer on which it rests make equal inclinations with HP. Draw the projections of the pyramid when the axis of the pyramid is inclined to HP at 40* and to VP at 30°. Solution . 99Problem .24 Ahexagonal pyramid 25 mm sides of base and.50 mm axis length rests on HP on one of its edges of the base which is inclined to VP at 30°. Draw the projections of the pyramid when the axis is inclined to HP at 452. Solution | | % a e 2 o | 9 o e Fy 7 Ss o 2 fo Se 100the base which is inclined to VP at 30°. Draw the projections of the pyramid when the axis is inclined to HP at 45°. ino 8 Solution Problem 24 A hexagonal pyramid 25 mm sides of base and 50 mm axis length rests on HP on one ofits edges of ofo] cid 0g vp, HP 100Problem 25 Ahexagonal pyramid 25 mm sides of base and 50 mm axis length rests on HP on one ofits edges of the base. Draw the projections ofthe pyramid when the axis is inclined to HP at 45 and VP ab 302. @ Solution iu Lon ‘atf) fal + + 101 beut Problem 26 A hexagonal pyramid 25 mm’sides of base and 50 mm axis length rests on HP on one of its comers of | the base such that the two base edges containing the corner on which it rests make equal inclinations with HP. Draw the projections of the pyramid when the axis of the pyramid is inolined to HP at 40® and appears to be inclined to VP at 45°. 00 P | Solution 102Problem 27 Ahexagonal pyramid 25 mm sides of basé and 50 mm axis length rests on HP on one of its comers. oF the base such that the two base edges containing the comer on which itrests make equal inclinations with HP. Dray, the projections ofthe pyramid when the axis ofthe pyramid is inclined to HP at 40° and a VP at 20°, P Solution 7 7 38,3 el ce 25 103 ™Problem 28 Asquare pyramid 35 mmsides of base and 60.mm axis length is base. Draw the projections ofthe pyramid when the axis appears 0 be Solution cS ig euspanded freely from a corner of its gist 0 bre 104 at ¢ fo] bis] be ze 3 " fo 4 4 #3 as soa \ Ng | iS 3 HProblem 29 Apentagonal pyramid 25 mm sides of base and 50 mm axis length Pan, ‘a comer of base. Draw the projections of the pyramid when the axis appears to be inclined to VP at 45°. Solution mo els 105/ Problem 30 Ahexagonal pyramid 25 mm sides of base and 50 mm axis length is suspended freely from a comer of its base. Draw the projections of the pyramid when the axis appears to be inclined to VP at 45°, Solution mo P motHal | pitty? |) problem 31 square prams thn sa stain ile oe ga a Draw the projections ofthe pyramid wtien the axis appears to be inp oP at 8. Solution 0 L > oe seen bid fo] fo] bie ofol| HP 107Problem 32 Asquare pyramid 35 mm sides of base and 60 mm axis length rests on HP on one of its slant edges. Draw the projections of the pyramid when the axis is inciined to VP at 45°. g Solution . See > 108rablem 39 Asquere pyramid 35 mm sides of base and 60 mm axis longth rests on HP onone ofits slant tiangular W the projections of the pyramid when the axis appears to be inlined to VP at 452. Solution a ono f | j | | h | \ : Lf \ Py 1 y i/ | \ ; / y } ty io o i = 28 5 a Eases 7 : . | 2 | Seay I= oe Ei ~~ ge Sif xfaces. Draw the projections of the pyramid when the axis is.inclined to VP at 45%, | Solution a 34 Asquare pyramid 35 mm sides of base and 60 mm axis length rests on HP on one of its slant triangular 6 110 a 09 se s/f xomnes 35 A pentagonal pyramid 25 mm sides of base and 50 mm axis length rests on HP on one of its slant ‘edges. Draw the projections of the pyramid when the axis appears to be inclined to VP at 45°, Solution a mop | y | | I | | g 1 2 i i= +——t 2 a a Ts o, 1 iS OF Se HP 11 iI / Probiem 36 A pentagonal pyramid 25 mm sides of base and 50 mm axis.length rests on HP-on one of its slant “edges. Draw the projections of the pyramid when the axis is inclined to VP at 45° Solution t 1 y 1 1 i | = 4 1 3 i o fo a t S ez > t 2 SED es ae a © e Ne <=: o | a % VP HP 112 x./Problem 37 A pentagonal pyramid 25 mm sides of base and 50 mm axis length rests on HP on one of its slarit triangular faces. Draw the projections of the pyramid when the axis appears to be inclined to VP at 45%. ~~ Solution a0 ie os | 3 | oo —o 3 a ia © E | St a |e >< 113Problem 38 A pentagonal pyramid 25 mm sides of base and 50.mm axis length rests:on HP on one of its stant. {angular aces. Draw the projections of he pyramid when heals is ingined to VP at 45%, ig Solution a Eee eee | . ‘ : fe eee z i \ A \ : g 2 e | = 4 Eee eee eee ee | Paes x 114Problem 39 Ahexagonal pyramid 25 mm sides of base and 50 mm axis length rests on HP on one of ts siantedges: Suton amr aiden ease pp ny cnt YP a4 Solution hTEd «a a Come du! lio | | { °° ° ” \ jy | \ ) 1 ind t T+ 2 H u @ 1e \ ue = + lo go fe x 115Problem 40 Ahexagonal pyramid 25 mm sides of base and 50 mm axis length rests on HP on one of ts slant edges. Draw the projections of the pyramid when the axis is inclined to VP at 45°. et Solution > WX \ ¢ e cle lot btfl foi] 28 VP HP 116Problem 41 A hexagonal pyramid 25 mm sides of basé and 50 mm axis length rests on HP on one of its slant triangular faces: Draw the projections of the pyramid when the axis appears to be inclined to VP at 45°, Solution ene f HN TiN / it \ Is oO s t t i luda a = = S 5 i 3 Pa 3 ° 2 2 2 7 se |e x 47Problem 42 A hexagonal pyramid 25 mm sides of base and'50 mm axis length rests on HP on one of its slant triangular faces, Dra the projections ofthe pyramid when the axisis inclined to VP at 45%. ree, Solution PEE EEeEPEEEEEEE Eee __45,88 cid 4 |b bte'lot) 1 al f a o bfe'l lot] fol VP HP. 118ww Py lem 43 A cube of 40 mm sides rests on HP on an edge which is inclined to VP at 30°. Draw the projections when the lateral square face containing the edge on which it rests makes an angie of 50°to HP. _ Solution 0B ‘ > 2 = 3 = f_ © g fH a a | 5 2| § 3 S =| 3 3 S S 2 sl. 2 S 5 e| = = — w S/S x 119 Neti2 t : & 8 a s i 2 8 ; 5 5 & j 4 2 E g 3 3 3 7 g 5 Z 2 é ; i £ 3 = é & . = a 8 a g & z 3 £ 5 g Ws 0] 2p < q ‘ ‘ Ly; D 00) {070 fon 0 o 1 |e uo} t & p \ i \ P op) | Dp cpp 3p | A fi di 7 iP upye Bd tupyo) Hy taua | dA 7 | | 2 | st i | i j i ; 2, e : s % — ae + Nope Wg a Aes op ae 121i Iblem 46 A tetrahedron of sides 40 mm is resting on one ofits sides on HP. This side is parallel to VP 1d 40 mm away trom it. itis tlted about resting side such that the base containing this edge is inclined at "Y 80° to HP. Draw the projections of the solid, Ef Solution & \Problem 47 A Hexahedron of 30 mm Sides is resting on one of its corners diagonals is perpendicular to VP. Dra ‘on HP such that one of its solid w the projections of the solid. _ Solution Fa 7 ray | cm oe i i Ht IN al ates POS fara) uh # Y | sh | . / \ ’ Ne af aC Ne 4 Y be 1 . t ‘ & ia eee a 122| | i lem 48 A pentagonal prism of base side 25 mm and height §0 mm is resting on HP on one of its base ‘Gomners such that the top most edge is at a distance of 60 mm above HP. Draw its projections, when its top view of the axis is inclined at 45° to VP, Also, determine the inclination of the longer edge of the prism to HP which contains the resting corner. Solution \3 ~ 2 7 FE Ne ‘3s \ 7 a \ a 2 yg € 4 2 a Se 5 : By \ SPN | — = 7 5 u x| s i #4 bANe q 3 yi 3 é [3 s|= ron 169m 9% PO D7_figeiem 49 A square pyramid of base sides 30 mm and height 60 mm is suspended by a thread tied to one | ‘of the corners of its base. It is then tilted such that the axis makes an angle of 45° with respect to the VP. Considering the apex of the solid to be nearer to the observer, draw the projections of the soli Solution apt aque i s Kf i 16) ~~ i | i J | 4) ye we af” i ¥ | WP - | i prabtem 50 Acone of base dia. 40 mm and axis length 50 mm is resting on HP on a point on the circum- J ference ofits base such that its apex is at 40 mm above the HP and its Jop view of the axis is inclined at 60° to VP. Draw the top and front views of the solid. Also, determine the inclinations of the axis when the base | is nearer to.the observer. Solution | « | r | | T | ; 4 ey 4 NP thal f Lee ow t hy arr ie oe M , i sh Jr ‘ © é : I, } & i ue os 124 ( ! | iCHAPTER 5 i | } i i DEVELOPMENT OF LATERAL SURFACES OF SOLIDS Problem 1 A triangular prism with one of its rectangular faces parallel to VP and nearer to it is cut as shown in Fig. Draw the development of the retained portions of the prism which are shown in dark lines. Solution i wat iu 126 Wop ¢ A cs A | T | | 1 7 7 Ei 7 It if i ‘DEVELOPMENT | ve. i x y io ba Le fet fel. 9 40 # Wt 420 4 BL BEES EH ta eee ete Al AX \M A & \ \ 78 y Problem 2 Asquare prism of base side 30 mm and axis length 60 mmis resting on HP on its base with all the vertical faces being equally inclined to VP. {t is cut by an inclined plane 60° to HP and perpendicular to VP and is passing ‘through a point on the axis at a distance 50 mm from the base. Draw the development of the lower portion of the prism. 2 Solution 23 A pc 4 A | 2 5 g DEVELOPMENT | ! ; | e al ) — fag He 1 al 125Problem 3 Asquare prism of base side 40mm and axis length 65mmis resting on HP on its base with all the vertical faces being equally inclined to VP. It is cut by an incfined plane 60° to HP and perpendicular-to VP and is pass! through a point on the axis at a distance 15mm from the top face. Draw the development of the lower portion of the prism. Solution per sss 34 | s 4 e ze) | | 2 8 g ‘ Deveuqeuent 3 / 1 I HP a a 5 a p Fopeeeeeee | 10 | © Por Problem 4 A square prism of 30mm side of the base and height 50mm is resting with its base on HP such that one ofits vertical faces is inclined at 40° to VP. Itis cut as shown in the following front view figure. Draw the development of the lateral surface of the prism. Solution 483 2 5 126Problem 5 Acube of side 40mm is resting on HP with its base on HP such that one of its vertical faces is inclined at 80° to the VP, Its cut by a section plane perpendicular to VP, inclined to HP at an angle 45° and passes through the ) midpoint of the axis. Draw the development of the lower lateral surface of the cube. Solution At, 44.14 14,64 34) 3 2 DVELOF 160 fENT Problem 6 Asquare prism of base side 35mm rests with its base on HP and two faces equally inclined to. VP, Draw the development ofthe lateral surtaces of the retained portions of the cut prism shown by dari lines in the Fig. Solution 127Problem 7 Arectangularprism of base 40mm 25mm and height 65mm rests on HP onitsbase wit the longer base Side inclined at 30° to VP. tis eut by a plane inclined at 40° to HP, perpendicular to VP cuts the avs at is mid height. Draw the development of the remaining portion of the prism. Solution Problem 8 A rectangular prism of base 30mm x 20mm and height 6Omm rests on HP on its base with the longer base side inctined at 40°to VP. Itis cut by @ plane inclined at 45° to HP, perpendicular to VP and bisecls the avis, Draw the development of the lateral surface of the'prism. Solution 4 Log 7 DEVELGPMENT | A Bere) reer oreeeeer eae 20 30 jee 100 128Problem 9 A rectangular prism of base size 25mmx4Omm and axis length 65mm is resting on HP on its base with the longer side of base inclined at 30° to VP. Its cut by a plane inclined at 40° to HP and perpendicular to VP and } passes through the extreme let comer of base. Draw the development ofthe lateral surface ofthe remaining portion of the prism. Solution / Problem 10 Draw the development ofthe truncated portion of the lateral faces of a pentagonal prism of 20mm sides of base and 50mm height standing vertically with one of its rectangular faces parallel to VP and nearer toit so-as 10 produce a one piece development. The inclined face of the truncated prism is 80° to its axis and passes through the right extreme comer of the top face of the prism. Solution f x 129: | i Problem 11 Aregular pentagonal prism of height 60mm and base edge 30mm rests with its base on HP. The vertical face closest to VP is 30"to it. Draw the development of the truncated prism with its truncated surface inclined at 60° to its axis and bisecting t. Solution ab Be & Db & A 60. 30 la ¢ , +h ee Problem 12 Apentagonal prism of 30mm side of base and height SOmm les with its base on HP such that one of the rectangular faces isincined at 40° to VP: Itiscut to the'shape ofa truncated pyramid with the truncated surface inclined at 30° to the axis so as to pass through a point onit 30mm above the base. Develop the truncated portion of the prism 180 as to produce a one piece development. Solution A B. ac BOo4 A DEVELOPMENT ___150Problem 13 Apentagonal prism of base sides 30mm and axis length 60mm rests with its base on HP and an edge of | the base inclined at 45° to VP. Itis cut by a plane perpendicular to VP, inclined at 40° to HP and passing through a point ‘on the axis, at a distance of 30 mm from the base. Develop the remaining surfaces of the truncated prism. Solution eet a ot a1 a at | 1 i / Ie es 4 3 : d : | 2 DEVELOPMENT ! _ 1 | e , i HF Ie c) > = A it 0. } \d | ' ia | (las { foes connie 30 Problem 14 Apentagonal prism of base sides 20mm and height 40mm is resting with its base on HP and baseedge parallel to the VP. The prism is cut as shown in the following front view. Draw the development of the lateral surface of the prism. Solution 131Problem 15 Ahexagonel prism of base side 20mm and height 50mm Is resting on HP onits base, such that one of its base edge is parallel to VP, The prism is cut inthis postion as shown in the following front view. Draw the develop- ment of the lateral surface of the prism. Solution ai big ote at A BG Os Fs A | ale 3 5 | g 8 ag 2 DEVELGPMENT le a ae ¢ 10! - 7 rik 1 ve a | TH “Tp a) oF ce le W B cD E F A ony (e).e4 20. TH ET aay aie m3 Db We Problem 16 A hexagonal prism of base side 25mm and height SSmm is resting on HP on its base, such that one of its base edges is parallel to VP. The prism is cut inthis position as shown in the following front view. Draw the develop ‘ment of the lateral surface of the prism. Solution Br co D, E, Fi Ae 5 DEVELOFMENT! ve He 132| j | | | Problem 17 The inside of a hopper ofa flour mill is to be lined with thin sheet. The top and bottom of the hopper are regular pentagons with each side equal to 30 mm and 22.5mm respectively, The helght ofthe hopper is 30mm. Draw the shape of the sheet to which itis to be cut so as to fit into the hopper, Solution Problem 18 Asquare pyramid of side of base 45mm, altitude 70mm is resting with its base on HP with two sides of the base parallel to VP. The pyramid is cut by a section plane which is perpendicular to the VP and inclined at 40°to the HP. The cutting plane bisects the axis of the pyramid. Obtain the development of the lateral surfaces the truncated pyramid. Solution| i Problem 19 Asquare pyramid base 40mm side and axis 66mm long has its base on HP and all the edges of the base are equally inclined to VP. ttis cut to with an inclined section plane so as the truncated surface at 45° to its axis, bisecting it, Draw the development of the truncated pyramid, Solution Problem 20 Atrustum of a square vertical and a side of its base is. lateral surfaces of it, Solution 8 _—_ 9 Pyramid has its base 40 mm sides, top.16 mm sides and height 60mm, its axis is Parallel to VP, Draw the projections of the frustum and show the development of the 134| Problem 21 A square pyramid of 25mm base edge and 50mm height rests with its base on HP with all fits base ‘edges equally incined to VP. Its cut by a plane perpendicular to VP and inalined to HP at 60°, passing through the extreme right comer of base. Draw the development of the lateral surface of the pyramid. Solution oe Problem 22 Arectangular pyramid, side of base 25mm x 40mm and height 50mm has one of the sides.of the base is inclined at 30° to the VP. Draw the development of the lateral surface of the cut pyramid, whose front view is: shown below. Solution 135Problem 23 A rustum of a pentagonal pyramid, smaller base sides 16mm and bigger top face sides 32mm and height 40mm, is resting on the HP on its smaller base, with one ofits base sides parallel to the VP. Draw the projections of the frustum and develop the lateral surface it. Solution “ Problem 24 Aregular pentagonal pyramid of side of base 35mm and altitude 65mm has its base on HP with a side ‘of base perpendicular to VP. The pyramid is cut by a section plane which is perpendicular to the VP and inclined at 30° to HP, The cutting plane meets the axis of the pyramid at a point 30mm below the vertex. Obtain the development of the remaining part of the pyramid. Solution 136Problem 25 A pentagonal pyramid, 30mm sides, with aside of base perpendicular o VP, Draw the development of the lateral surfaces of the retalned portion of the pyramid shown by the dark lines in the following figure. Solution Problem 26 A pentagonal pyramid of 30mm edges of base and S0mm height rests vertically with one ofits base ‘edges parallel to VP and nearer toi. tis cut as shown in following figure. Draw the development of the lateral surfaces cof the upper portion of the pyramid. SolutionProblem 27 Ahexagonal pyramid, base sides 25mm and height 60mm, is resting with its base on HP and an edge of base inclined at 40° to VP. Itis cut to the shape of a truncated pyramid with the truncated surface indicated inthe front view at a point on the axis 20mm from the apex and inclined at 40° to XY. Draw the projections and show the development ‘of the lateral surface of the remaining portion ofthe pyramid. Solution Problem 28.A hexagonal pyramid of sides 35mm and altitude 65mm is resting on HP on its base with two of the base sides perpendicular to VP. The pyramid is cut by a plane inclined at 30° to HP and perpendicular to VP and is intersecting the axis at 30mm above the base. Draw the development ofthe remaining portion of the pyramid. Solution 138Problem .29 Ahexagonal pyramid 25 mm side of base and axis 65 mm long is resting on its base on HP with one ot the edges of the base parallel to VP. Iis cut by a vertical section plane at a distance of 8 mm fromthe axis towards right ‘side. Develop the lateral surface of the left part of the pyramid. Solution h\ M\ F | \% 2 \ we LLNS, HP al or i ice ts I a a la Problem 30 Ahexagonal pyramid of 30mm base sides with a side of base parallel to VP, Draw the development of, the lateral surfaces of the retained portions ofthe pyramid cut by two perpendicular planes shown by dark lines: the Fig. : SolutionProblem 31 Avertical cylinder of base diameter 45mm and axis length 60mm is cut by a plane perpendicular to VP | and inclined at 50? to HP, is passing through the centre point ofthe top face. Draw the development ofthe lateral } surface of the cylinder. Solution bel e Problem 32 Following figure showis the front view of a model ofa steel chimney of ciameter 6Omm made from fat thin sheet metal fitted over an inclined plane roof, Develop the portion of the chimney. Solution aor ben 140Problem 33 A vertical cylinder of base diameter 60mm and. axis length 60mm is cut by a two planes: which are perpendicular to VP and inclined at 45° to HP and passing through either side the centre point ofthe top face, Draw the development ofthe lateral surface of the cylinder. | Solution ic | f 4,(10) BINS | pany + Nes, ht Me) | Problem 34 Apipe made of using a half tubular (circular) witha half square in shape is cut as shown in the following | figure. Draw the development of the lateral surface of the object. we Solution eg 141Problem 35 Develop the lateral surface of the cylinder of 40mm diameter.and height 6Omm which is cut in the following way. Solution Problem 36 Acone of base diameter 60mm and height 70mm is resting on its base on HP. Itis cut as shown in the following figure. Draw the development of the lateral surface of the remaining portion of the cone. Solution 142Problem 37 Develop the lateral surface of the cylinder.of 4mm diameter and height 60mm which is cut in the following way. Solution $2 42 12 13)¢ 60 2\(r0" Af) x PLA fe HPO“ allairelk afi esi Rg le / Zt ’ Ze ra 4 x a i Problem 38 A cone of base diameter 60mm and height 70mm is resting on its base on HP. Itis cut as shown in the following figure, Draw the development of the lateral surface of the remaining portion of the cone. SolutionProblem 39 Draw the development of the lateral surface of a truncated vertical cylinder, 4mm diameter of base and height Somm, the truncated flat surface of the cylinder bisects the axis at 60° to it. Solution B02. 1gy| (7 7 AG) hs 3 4|(10) 4 Ho | “ 0 7 fa f 7 te | “AB CD CE KU A Problem 40 Develop the lateral surface of the cylinder of 40mm diameter and height 60mm cutin the folowing way. Solution 4,(10) 4 t 7 a} anyZ_1 New 8| Mt 24 a i seal 8 tai er - Ae cD 0.47 ; 125.66 j 144Problem 41 A right cone of 55mm diameter of base and 75mm helght stands on its base on HP. Itis.cut to the shape of a truncated cone with its truncated surface inclined at 45° to the axis lying at a distance of 40mm from the apex of the cone. Obtain the development of the lateral surface of the truncated cone. Solution Problem 42 Draw the development of the foliowing truncated cone, Solution ; al buh) T aif) le : | Nui | | \ | } | 3 oo NS / 1 ! 0 i i 145Problem 43 A hexagonal pyramid of 30mm sides of base with a side of base parallel to VP. Draw the development of the lateral surfaces of the retained portion of the pyramid which is shown by dark lines in the following figure. Solution ® Problem 44 Develop the lateral surface of the'cylinder of 40mm diameter and height 60mm which is cut in the following way. Solution 17) 146