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321 views56 pagesMensuration
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Praveen KumarCopyright
© © All Rights Reserved
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eraser
Mensuration
In the given figure, ABCD and BEFG are squares of
sides 8 cm and 6 cm respectively. What is the area
(in cmv) of the shaded region?
“@7¢ apf, ABCD wa BERG aR: 8, we 6 FH
ora i orate ara donee (SH wT?
{—»
tay12 (eis
(10 (16
PORS is a parallelogram and its area is 300 cm’
Side PQ is extended to X such that PQ = QX. If
intersects QR at Y, then what is the area (in o
of triangle SYR?
PORS UF WaER aga & Ta
WT PQ aT x TER Te
XS, OR WY
ane?
and QT inter-
what is the value (in
PORST Vale PRT QT HEE FTX
shred B, ACTA ATA (fet H) TE?
(A) 98. (B)90
(72 (0) 108
4, In the given figure, ABCDEF is a regular hexagon
whose side is 12 cm, What is the shaded area (in
em’)?
“dog angi ABCDEF UH FAYE forest ya 12 SH
& sarecaten are a Servet (Ae) A ee?
>
(A) 54/3) 36/3 (C) 48y3_ DI 523
‘ABCD passes through the centres of the three
circles as shown in the figure. AB = 2 cm and CD =
Tem, Ifthe area of middle circle is the average of
the areas of the other two circles, then what is the
length (in em) of BC?
ar Pe omega Hever er, ancl
aaa ia - 2 ah wercp=1
aor, ri att areca
8) (Vo)+1
) (V6)-3 (0) (V6)+3
A= Area of the largest circle drawn inside a
square of side 1 em./1 34, spar aa =i 8 at
anise
B= Sum of areas of 4 identical (largest possible)
circles drawn inside a square of side 1 cm./ 1
eh, para a a are a mera ae a)
areca
C= Sum of areas of 9 identical (langest possible)
circles drawn inside a square of side 1 em. /
1, pera at Hg area pe Carre aE aa)
Saami arin
D=_ Sum of areas of 16 identical (largest possibie)
circles drawn inside a square of side 1 em. /
1a opr at a 16 Beep (wa a I)
ae tre im
Which of the folowing is TRUE about A, B, C and D?
Freon H-8 A, B, cma De aia a ATE?
(AsBec>D
BAcBeCB-coD
(©) No option is correct/ WHE fewest wet =
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1.
Mother's weae afera + aififet
A prism has a square base whose side is 8 cm. The
height of prism is 80 cm. The prism is cut into 10
identical parts by 9 cuts which are parallel to base
of prism, What is the total surface area (in cm) of
ail the 10 parts together?
“fear at fra yr 9 Be fo tS 80
Fh, few cre Hier 9 seria 10 nite ara TAT 10,
vita ga free pe yea Bae (deh) aa?
(A) 4260 (B) 2560 (C) 3840 (D) 3220
A cone of radius 90 om and height 120 em stands
on its base. It is cut into 3 parts by 2 cuts parallel,
to its base stich that the height of the three parts
(from top to bottom) are in ratio of 1 : 2: 3. What is
the total surface area (in cm‘) of the middle part?
em 90 Heh fe ae 120 eh, Sead ae vp Te ET
rc erer ee see ee 2 aT A 3 HT ee eR
sare en & Patt at See (eC a a Si) =I
srs 13 & rea rah ee dere Aw) a?
(a) 14600 (B) 16500
(©) 17800 (D) 18500
‘The curved surface area of a cylinder is 594 cméland
its volume is 1336.5 em®, What is the height (i
of the cylinder?
a4
(©) 24.
A hol iffer-
of thi the cylinder is
28 hollow cylin-
the inner and outer
ae rer eres ar ee
382 Sh? a ga ter a SE
28 fh ae wera Aer a ga Tea daw 2640
“Sait &, der ater cen a fae (A, ) Te?
(A) 4,6 (B) 10,12
(C) 8,10 (D) 6,8
‘A solid metal sphere has radius 14 om. It is melted
to form small cones of radius 1.75 cm and height
3.5 em, How many small cones will be obtained from
the sphere?
ep oy at hfe 14 Sh ere 1.75 Be
‘rea aan 35 ah, Sra ae aig A ar a
fa ait vig ae or aa?
(A) 512 (B) 256
(C) 1024 (D) 2048
12. A metallic hemispherical bowl is made up of steel
The total steel used in making the bowl is 342
cm’. The bowl can hold 144x em water. What is the
thickness (in cm) of bowl and the curved surface
area (in em’) of outer side?
sound eng an er ovina acho aera a a
ah pe scan Beh ce i Pa RTH
gn oh? et om aren eRe ee Ce me
art ce a ta ere (Sh) aT?
(A) 6, 1620 (B) 3, 1620
(C) 6, 81n (D) 3, 81m
‘There is a box of cuboid si
of the box is 20 em and lange
of the following can be vol
13.
6, whose side is & om. If
fa is 16 em, then what is the
fin cm’) of the pyramid?
sorercor tera ap 8 eh & ae Pratice
163. @, ah faite ape yea are (AH?
at?
(a) 64(Vi7 +1) 8) 32(VJI3-+1)
()o4(V3 +1) (D) 32(V5+1)
18. In the given figure, ABCD is a square of side 14 em.
B and F are mid points of sides AB and DC
respectivety. EPF is a semicircle whose diameter is
EF. LMNO is a square, What is the area (in em) of
the shaded region?
i owpfa, BCD 14 2A, yar eR nd tLe ae
Jes: AB Ta DC YT we fry tL nPP, ew KE
fener eae BF tILMNO wear rorfies Mero dar
(HH) ee?
(a) 108.5,
(c) 70
Boss
(D) 120
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17.
18.
‘Mother's Advance Maths + Mensuration
In the given figure, ABCDEF is a regular hexagon
whose side Is 6 cm. APF, QAB. DCR and DES are
equilateral triangles What is the area (in cm’) of
the shaded region?
Od anpfa ¥, ABCDEF we ways & forrat qT 6
ri, BLAPR, QAB, DR aH DES Hay fay saree
var ae eet (ae) Te?
°
D Is
zl Ic
s R
(a) 243 (8) 18/3
(©) 72N3 (D) 3693
Length and breadth of a rectangle are 8 om and ¢
om respectively, The rectangle is cut on its foul
vertices such that the resulting figure is regu
In the given hgure)
PORS is a square
are four identical
{in cm) of all all squares?
Sind onphd, ce qaat feat LAV3 at PORS oH
wi 8 1EPGH, ABCD, WXYZ 91 LMNO @R WAR 7H |
at die aif apa ara (Ah A) at?
HH, ABCD, WCYZ and LMNO
jares. What is the total area
(a)31.36
(c)62.72
(By128.44
(D) 156.8
19.
In the given figure, AB, AE, EF, FG and GB are semi-
circles. AB = 56 cm and AB = EP = FG = GB. What is
the area (in cm'B} of the shaded region?
ig angft#, AB, AE, EF, GTA GB sign 1 AB ~
56 @h, ar AE = EF ~ FG = GB #1 waif si aT
Serpe (Beh?) ak?
(aj414.a6,
(c} 406.48
arena ae ve ee
maga ene?
@isiea
(D)1:7:20
Radius of base of a hollow cone is 8 cm and its
height is 15 em, A sphere of largest radius is put
inside the one. What is the ratio of radius of base
of cone to the radius of aphere ?
rer ire vig sree a fae g aah, sora Sa 15
eb. rad ah aren or arse vig Herre |
sep ore al rear th a fea a sept?
@is:3 Ban
(2a 7:3
‘The ratio of curved surface area of a right circular
cylinder to the total area of two bases is 2:1. If the
total surface area of the cylinder is 23100 cm? then
what is the volume (in cm®) of cylinder?
orga er enc deren a ep ae se
Spe pera 1 ae sere ge ge eae 29100
eho 8, aha wr orga (Heh? H) ek?
(a)247200 1B) 269500
(¢}312500 (0)341800
A solid cylinder has radius of base 14 cm and height
15 cm. four identical cylinders are cut from each
base as shown in the given figure. Height of small,
cylinder is 5 cm What is the total surface area (in
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cm) of the remaining part? 26.
Tr ota Se STI I aT 14 SH, Te Saw 15 AH,
21a fe angie a cain en? fe ee wee or a
War ae Fe Fale For at Hae 5 A 2 aT a aT
Mother's weaie afera + aififet
pea pets tree (ArH) Tt?
(ay3740.
(e)a124
10 identical solid spherical balls of radius 3 cm are
melted to form a single sphere. In this process 20%
of solid is wasted. What is the radius (in cm) of the
bigger sphere ?
3 BR, fear ah 10 WH a Tires Hel a free ee Tite
arr are 1g wT 20% Sta sae eT oT E aS HT
i fo (ah) wae
(ay 24
os
‘The radius of base of a solid cylinder is 7 em and its
height is 21 cm. It is melted and converted into
bullets. Each bullet is of the same size. Each
consisted of two parts a cylinder and a hemisy
fon one of its base. The total height of bullet
om and radius of base is 241 cm. Approximat
we ata Fen ste at
aera H) eT?
(ay as(Va)e1
(©) 28[6+(V3)
(3432
(D) 2816
(Bz
D6
Fe area (in em) of the pyramid?
Sar fs ont a cain Fe Ha a OH a
‘nga Ferre XYZ rena Ew HT 16 eB
X,Y 2 a ai ee for & i Ftere a e TT
wy 24[4+(8)]
om) 323+(5)]
2.
Inthe given figure, two squares of sides 8 cm and 20cm
are given, What i the are (in cn) of the shade part ?
id orgy, sth, gar aot, gras aia fea
Bvt ra Serer (BH) TE?
7 ABCDFE is a regular hexagon of side
snd Rare the mid points of the sides AB, CD
EF respectively. What ithe area (in cx) of triangle
Gin opt, ABCDFE WH aH ey & fare ToT 12
Beh 1p, Quen RaRAR: TH AB, COTE EF ae mA fry
#1 feya poR aa Save (Aria) ene?
Ho»
@
F ‘
(9) 276 ® s1y3
© 543 (0) 546
A manis running at the speed of 20 km/hr. What is time
(in seconds) taken by man to cover one round ofa circu-
lar garden of radius 250 metres?
‘oe maf 20 farts wer at aa a She er BO
anita farsi fea 350 diet @, Sto ee A oafaa er
‘feraray (Sars H) fern were?
(aaa (8336
(©)3% (D)376
HEAD OFFICE : J-7, Himmat Nagar, In front of BIG Bazar, Gopalpura Pulia, Jaipur-302018
(0141-2711689, +91-7073909991 | www.motherseducationhub.org ‘Mother's Advance Maths + Mensuration
31. Inthe given figure, four identical semicircles andl drawn,
in-a quadrant. XA’= 7 em. What is the area (in cm) of
shaded region ?
“thd enpta ar wren ordeal at ee Tae ad Tet
aaa xa = 7B Bore Tr eet (Ht
H) amt?
D,
¢
xa 8B
(a0 (140
on Dyst
32. A regular hexagonal base prism has height 8m and side
of base is cm. What isthe total surface area (in em of
the prism?
er aH Wea sree ae fs at Sra 8 oh, @ oe STE
ar set oer et Sever (Ah)
#2
(a)34(3+ V3) (3+ V5)
© 48(4+ V3)
22 Acubeisy i
awem, nd
vertices of hati the
length tin
TRA TE ‘wen Sra 10 Br.
% saaraomme, ag & Sr SRE
ven fits a carer att # erat ara
wean (Si, H) ATE?
(ays Be
os (mye
34. A cylinder of radius 4.5 cm and height 12 cm just isin
another cylinder completely with their axis perpendic
lar. What is the radius (in cm) of socond cylinder?
ep tera fiers fran 4. eh war Soe 12 Sh, AE
rea er sh on Ae oe ye ee A ae Pet
aren gat era ah fen (Be A) ee?
(A)5 (B)6
(15 (D)75
3, A right circular cylinder as height 28 em and raivs of
base 14cm. Two hemispheres of radius 7cmeach are cut
from each of the two bases of the cylinder, What i the
total surface area (in cm) of the remaining, part?
co a ster era Seat 26 Se en see a aa
13h, RHA sea 7 HA, ora a SrA
ae ad #1 wt ar ge Tea Saw (Se! A) aT
am?
(arse wr
(C) 3296 (D) 4436
‘Two spheres of equal radius are taken out by cutting from,
asl eube of side (12+ 418) cm. What i the mic
cm vole inc) ofechapherg
war fem art at wet at oe
(12448) aed. treme Fre are
ler, hem SPREE and
Height of each toy is
tal surface areas of
rated 2 Be tere oh
ge da dare a aA: STA TE?
fayazs:[(v2)+1] eas: [2+(v2)]
(4:8: avo (p21: (1+ V2)
A solid cube is cut into 27 identical cubes. What is the
percentage increase in the total surface area?
we da a 27 wawT or A ae 8g Tet
apres a fara afawra at af et?
(a)150 (B) 200
(©) 300 (D)250
‘A rogular square pyramid has sido ofits aso 20 cm and
height 45cm is melted and recast into reglar trianglar
pyramids of equilateral base of side 10 cm and height
10V3 cm. What are the total numbers of regular trian-
gular pyramid?
1p am arian Prats Fath oma a aps 20 SHA, ae
Sad a5 ht, a franca Paya Feats eT
“ara Fs seg reac a pa 10 eh, we SE 10/3
eb, 8 a fea feat at pete ee?
(A)24 @20
(27 (D)28
In the given figure. POR is an equilateral triangle
with side as 12 em. and T are the mid points of
the sides PQ and PR respectively. What is the area
tin cm of the shaded region?
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42.
Mother's weataaferat + aif
tnd opi oR eH arg Pras fares yor 12 ae.
1s a7, mH: aT PQ Ta PR forge | wrafe
sara ata (eH? HF) ae?
P
ir
9 R
(ayo iw
(Cy 93 ©) ws
ABCD is a rectangle. P is a point on the side AB as
shown in the given figure. If DP = 13, CP = 10 and
BP = 6, then what is the value of AP?
ABCD 1 aaa #1, PAT AB Ter rg eters ae
angie # eatarrar# raf DP = 13, P= 107 BP= 6
Adapt?
tT R
$
(a) 1623 (8) 2163
(c) 108 (msn
In the given figure, ABCD is a square, BCXYZ is a
regular pentagon and ABE is an equilateral triangle.
What is the value (in degrees) of ZEBZ?
47.
dnd aria, ancy ural t, acxvz we aH rage
"War ABE Tem rag PS e | ZeBz TI (Feit) aA
@
x
(a) 102 f
() 78 (0)
In the given figure, 3 semi ar yn three
sides of triangle ABC,
(A) 588 (B) 324
(C) 294 (D) 286.
‘The sum of radi ofthe two citcles is 91 em and the
difference between their area is 2002 om?, What is
the radius (in cm) of the larger circle?
Spt st feat ara 91 Se Ran see are ee
ie 2000 He? # a a fa CAH) aT?
(A) 56 (B) 42
(63 49
{A right triangular prism has equilateral triangle as
its base. Side of the triangle is 15 em, Height of the
prism is 20/3 em. What is the volume (in em!) of
the prism?
op ry eee far ee a Fg BPE
citar as ahem at Soe 205 ¢ ar eT
(Re H) ene?
(ayii2s (3)6750
(c)4500 (p) 3375
‘The height of a cone is 45 om, It is cut ata height of,
15 em from its base by a plane parallel to its base.
Ifthe volume of the smaller cone is 18480 cm’, then.
what is the volume (in em®) of the original cone?
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(0141-2711689, +91-7073909991 | www.motherseducationhub.org 49.
50.
51.
52.
‘Mother's Advance Maths + Mensuration
ep tig ah San 4s ahi, 8 17a TATA 15 SH, STH TE
‘BR Sa saree Ae aR aT!T eT a ee eR oT APT
18490 Si. &, ae siege sas (Heit?) H aT?
(a) 34650 (B)61600
(36960 (0}62370
The ratio of the curved surface area and total sur-
face area of a right circular cylinder is 2: 5. If the
total surface area is 3080 em’, then what is the
volume (in cm’) of the cylinder?
ae ee FeIPAR ae BT Sawer en Fer yea
Soret ar ayaa 2 5 2 ale Fer TSH Aart 3080 Teh?
hae a rae (Ae) Te?
(a) 43126 (B) 38226
(©) 4522v6 ©) 4642V6
The radius and height of a solid cylinder are in-
creased by 2% each, What will be the approximate
percentage increase in volume?
ee She era a er ae Sr tr 290 8 A TT
Brae Herne Fett fe a as?
(A) 6.76 @) 588
(c) 612 (0) 3.34
A sphere of radius 21 ¢m is cu
by 3 cuts (1 cut along each
total surface area (in em)
of side 14 cm. The
art of the two oppo-
fat is the total volume {in cm)
of the cube?
na am are anita 1 we 14 Aa.
{a ara ata a a rea ae | spe ST a eT
ferrite renee 3 TS a a ET aT HEA STAT (TA)
Fant?
(a) 1556.33 @) 8985
(C) 1467.33 (0) 1306.67
Identical cubes of largest possible size are cut from
‘solid cuboid of size 65 cm x26 em x3.9 cm, What
is the total surface area (in em!) of all the email
cubes taken together?
vee che aa fara 65 Ae x 26 Sh. x 3.9 A BA
ofeeres sort ary are ares af et ere TAT Ast ae
seit at fern ga yea dae (Aah? A) wT?
(A) 30420 ®) 15210
{c) 20280 (D) 16440
53.
A regular triangular pyramid is cut by 2 planes which
are parallel to its base. The planes trisects the al-
titude of the pyramid. Volume of top, middle and
bottom partis V,, V, and V, respectively. What is
the value of V, V1 V2
‘op Proaren Ftng a1 ar St se oe Ha,
re rer en er faire at Sed wir et
sw ooh, wea oer Prada TIT AME Vy, V,
env #1V,:V, Vara Te?
(A) 1:8:27 (B) 1:8:19
(C) 2:9:27 (D) 1gmi9
PQR is a triangle, whose area 18/180
point on side QR, such that PS
tor of ZOPR. If PO: PR = 2: 3,
(in cm*) triangle PSR?
pameter fry &, Frere 4
BCD is a square. EFGH is a
‘by joining mid points of sides of
area (in cm?) of square ABCD?
ie angi, ncn wat 1 ABCD a yi x
fags stemen i ero ara ERG PGT
Spagetti iMNO FITTER TTA
arr LMNO Hsien Peart afe re rer 38.5
4, fart ABCD ar aavet (eH A) aE?
E
: 5
yNw
| )
K
so
(ayo i196
(G22 ins
ABCDEF is a regular hexagon of side 12 cm, What
is the area (in cm®) of the triangle BCD?
ABCDEF 12 St, SaTaTeN eR aATEYRe |S ECD
Seamer (ae HD eT?
(a) 183 B) 25
(C) 36V3 (D) 423
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Mother's wearer afta + aiff
PORS is a square whose side is 16 em. What is the
value of the side (in cm) of the largest regular octa-
gon that can be cut from the given square?
PORS 16 Heh, Sr ren Te at et ane oT
“ae rt ar se ah Tare (Be, H) Te?
(8-42 8) 16-83
(© 63-vie ©) 16-82
In the given figure, PORS is a rectangle and a semi-
circle with SRas diameter is drawn, A circle is drawn
as shown in the figure. If QR = 7 em then what is
the radius (in em) of the small circle?
“Qing opie 8, poRs we sed ¢ aa SR one aTeH ee
asin are ra | her fir arpa ate en fe
a aren mee ae QR = 7 et, te gH at far
HH) Tene?
2
Rk
(8) 21st ®B) 2-2
(©) Both 21+ 143 and 21 — 143
(D) None of these / 74a 1 wet
In the given figure, PO!
dius is 7 cm4A
(a) 385
() 154
(@) 308
(0) 462-308V2
A prism has a regular hexagonal base with side 6
com. If the total surface area of prism is 2163 em’,
then what is the height (in cm) of prism?
“we fr ee wr 6 Be. pT Te EMEA E ae et
arg yaa terre 216 V5 St, aon a Sak CH
yen?
(A) 3y3
(c)6
Boi
os
61.
‘The radius of base of solid cone is 9 cm and its
height is 21 cm. It cut into 3 parts by two cuts,
which are parallel to its base. The cuts ate at height
Of7 em and 14 om from the base respectively. What
fs the ratio of curved surface areas of top, middle
and bottom parts respectively?
‘er de eg ste at ren 9 Bah, oem se Sr 21
Shh. 13a dace, wt ove aa 2 a 3 aa are
Tre ers area see: 7 A ae 14 Ae, a Shes eA
aera: Sat, er oer Fraet arit & ae Sts aera
arg wt?
@ ie
( 1:3:9
A right circular eytinder has
fadius ab 7 cm. The eylindes
@B)1:3:5
eam aa dene ae a STATA 1:7
geste oer ae ea I SATA 187 : 770 FF
se a from ae Sard wr STG TE?
@ 58 ) 49
©) 3:7 (D} 7:10
The ratio of total surface area and volume of a
sphere is 1:7 is. Ifthe larger sphere is melted and
formed into smaller same size sphers and radius of
the smaller sphere is 1/6 of the larger sphere. What
is the sum (in om) of curved surface areas of all
small spheres?
wap mt pee ae ea Seg 7B eA
2 Ferree ae a Se te aa dE a Sa
ie fee a at Fara 6k ra we
gets are aa (SF) ae?
(a) 31276 (B) 30194
(©) 25182 (D) 33264
A hemisphere is Kept on top of a cube. Its front view
is shown in the given figure. The total height of the
figure is 21 cm. The ratio of curved surface area of
hemisphere and total surface area of cube is 11 : 42.
What is the total volume (in em) of figure?
“er aaete e TC Ce e& eaP RTE Te SaTA
Fi cater rent | orp at pe Soar 21 ae. tort
cae cha dearer wee re yes eae STA
242% sapfa a pet sarees (Set) Fae 7
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(a) 9318.93 @) 9462.67
(c) 3154.67 (0) 3248.33
A solid cube has side 8 cm. [tis cut along diagonals
of top face to get 4 equal parts, What is the total
surface area (in cm} of each part?
eens ys teh, tae aoe wae Pit we we
sari rer ar acer oe age gestae (2)
fiaat?
(A) 96 + 642
(©) 964 482
(B) 80+ 62
() 80+ 48/2
67.
A regular pyramid has a square base. The height of
the pyramid is 22 em and side ofits base is 14 cm.
Volume of pyramid is equal to the volume of a
sphere. What is the radius (in cm) of the sphere?
“a faire ar ar at 1 Fs =e So 22
St aen set oe ah yor a4 Sr. Bate an oer
ra
aia ores ee aa
(a) 9
merger gare apd amr é era, yee Sage
cere at ert at en fr npr eee rk A
warm (Set a) ere?
: lo
(a) 13/17 @uyp.a
(cy 19/31 (0) 15/19
‘The base of a prism is in the shape of an equilat-
ral triangle. If the perimeter of the base is 18 cm
and the height of the prism is 20 cm, then what is,
‘the volume (in cm’) of the prism?
ep Br ar omen a Pans CAE ae eT
‘fer 18 eh cen ow at Se 20 a &, a Be
carer (ih) ek?
(4) 60V3- 8) 30V3
(€) 1803 ©) 120y3
70. The height of a cone is 24 cm and the area of the
base is 154 cm, What is the curved surface area
{in cm*) of the cone?
wa vig at Sead 24 ahh. tae area aga
Siig ae Te oe sl
(A) 484
(c) 525
a. circular cylinder
3:2 ta tera ora 4312 9
3 ori swat daw (RHP) wri ee?
(B) 308
oy616
A solid hemisphere has radius 14 om. It is melted
to form a cylinder such that the ratio ofits curved
surface area and total surface area is 2: 3. What is
the radius (in cm} of its base?
cop are orth at a 14 aah, Be Pere a
Fa a rer one fe See erg x eH FT
aged Serre orga 2: 3 reer sere Br (A
Hane?
1
(a) Be
2 en
B eB
‘A cuboid has dimensions 8 om x 10 em x 12 em. It
is cut into emall cubes of side 2 om. What fs the
percentage inerease in the total surface area?
ET SM 8 Se, « 10 Ta, 12 Aah Ba 2 Teh
spare a2 a 8 ere orn ger sia Grower Pw
MW
Og
©
afar af eet?
(A) 286.2 (B)314.32
(C) 250.64 (D) 386.5
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A pyramid has a square base. The side of square is
12 cm and height of pyramid is 21 cm. The pyramid
is cut into 3 parts by 2 cuts parallel to its base. The
cuts are at height of 7 em and 14 cm respectively
from the base. What is the difference (in cm*) in
the volume of top most and bottom most part?
ew frais om sree wm ee ar wh pT 12 Se a
frre ai San 21 aoe | Prats aT sae STAR TATE
2 anit a arer wren & | wera sree B eM: 7 Ae eT 14
anh, at Sak We) aaa oe oa aaa a a
area a ore (AY) Hae?
(a) 872 (B) 672
(C) 786 ©) 918
A
va2 a3
a) c
In given Diagram, Four circles of equal radius pass
tghrough centre of circle of radius 15 cm then find
area of shaded region.
aie 15 Se, fre are ae a ae aa eee TT
Temata afe aet EE Tse Eat eras oI aT
are ve eT?
(A) 169-250
(©) 225m - 450
(B) 1961 - 350
(D) 1252 - 550
77.
Three circles of equal radius of '12'cm pass through
centers of each other then find area of shaded region.
diana r get ee a ae Pe fe
a oraitea om ar area aa aif
(A)72n (l
(O36 + S
\\
yj
figure, ABCD isa square of side 14 cm.
ng 'D' and 'C’ centres, Two quater circles of ra-
dts 14 cm is made and an another half circle on DC
taking DC as diameter is also made, then find differ-
ence of area of two shaded areas.
“aft feta Fea ABCD er 14S. arate DIT
(Cale are we tha qa ara 12 Fao Fe
aaa YT DC a1 Fe fry 2 torrid a & are
a oe a em?
(ay42
(O36
(B)38
(D)35
Ina equilateral triangle AABC, ACLBP and BCLPQ.
Find ratio of area of APRB and APQC. IFRP | BC
wrag AABC # ACLBP #4 BCLPQ @ | eraiféra APRB
“wa APOC tare arg AE RP BC |
(A21 (3:1
O4n (D)5:2
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Two circles of radius 3.¢m and 6 cm intersect each
otherin a such way thal their common chord is of
‘maximum ., Then whatis the area of the region that is
common to the circles ?
Daa er gata ara on # acl ate sara:
sab ad aint ag 70a Re6em WUE Tae Pear
= Sem era aro ar eh?
(A) 2In- 9/3 (7 -oN8
3in
© 360-98 (= -N3
81.
pre a
82.
cm. A smaller circle is,
BCD is a square of side 'a
Coa as shown in figure find area of the smaller
Stew ABCD Ap ae eat a pera eR et
Pep ae yee ee reer terres
que a wae eT?
na a’ na’ ma?
Oia Os Obs ice
A B
a
83.
Ina Rectangle ABCD is semicircle is drawn on diam-
eter DC where DC= 14 cm, the find difference of ares
of shaded region,
ara ABCD H DCI Sy AR
‘Wel ara DC = 14 te a orate
ener?
jem? (B) 42cm’
84, P
8
a trapezium ABCD ABIDCand BD 1. AD and AC 1
If AD=BC= 15 emand AB= 25cm then find area
of Trapezium.
wre apis ABCD 4 ABIDC 741 BDL AD Wa ACL
BC af AD = BC= 15 cm ait AB = 25 cm @ #t Bacla
sais an aera aif |
(A) 156 cm? (B) 178 cm?
(C192 cm? (D) 189 cm*
upd
y
‘A Pyramid of square base of side "12' cm and height
"21' em which is cut along, its height parallel to its
base in three equal heights then find area of middle
region.
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‘ee rene ets seh pa "12" Bei are 21°
it fea dae Sad a ee oR aE TTT
sete wR Ys Sew eM eT?
(9) 6497 ge) ATT op
aes
(© 8477 om OS om
‘
Do m1
InRight anyle triangle ABC where B= 90° and BDEF
iSsquare. Al
OfAABC.
AABC4 B aaa # | BDEF WTI e | AE = 7.57. war
‘AC = 18h a1 fs ABC a area a
(a) 67.861
(389987
'=7.5emand AC=18¢m, Then find area
(8) 36526
(0) 76.621
3: QAP: FC=1:5and BD
‘of areas of EFCD to ABC.
=312, AF: FC=1:53 BD: DC
= 4:3 8 a aapfa EFCD tar Pra ABC % ar a
agra ara
(ayag:71 (B)54:79
(47:70 (D)50:81
¥ e
F ©
Inthis given figure ABCDEF is a regular hexagon of
side 12cm, P, Q, Rarea the mid points of AB, CD, EF.
Find area of APOR.
‘dig snp, ABCDEF we array fire pat 12 A
ZIP, Q, R qarsit AB, CD, EF % 9 fry @ PTA POR
ar orien Sear eat?
(A) 813
©) 723
(8) 643
() 25V3
Two identical circle of Radi
tre of each other then
E Qa
A pyramid of base regular hexagon of side 2a'em. If
D
5a
slant edges of that pyramid is “> cm then find total
surface area of the pyramid.
‘ue Free Farrer amare 20" A spat aren wee LAT
oe ae are eat on 2 a ea a
Frafere an ape ys Soave ara AIL
(A) 6a" (21-3) (8) 3a* (21 + v3)
(©) 3a" (V21 +23) (D) 6a*(V21 + V2)
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91, Ina rhombus, sum of two diagonals is sec® and pe-
rimeter is ‘2tan0" then find area of that Rhombus. DD
caer araghfa 3 ar Feit 1am soco aera WCET A
‘lana! ater dere aa fi > /
1 5
wt @?
2 1
oF 5
c
2 | ft ©
k cm
fo
5
A )
ABCD are the vertices ofa parallelogram where P,
R Sare themidpoints of AB, u
Find the ratio of area of shad
ABCD FARR apis * vir 2 1
BC, CD, DA%
um &
(a)2:3
ous
a Ifradius of Bigger Circle= r, then find Ratio ofshaded.
7 area A toshaded area (B, +B.)
oer as 70 ah Bear & at rife om A sik eras aT
(+8) a saTa AT
aon
( g(viy ona
3
5 P © ®) g(2+1) - 20-3
Inthe given figure, Base BC & height AD ofa triangle 4-6
ABC is 8.cm, Find the area of shaded part region. oO a(2+ 1) 430-4
‘feat 74 fers # AABCH sree BC 141 Sens AD eri 8 cm
8 writes am ar are are Fifa 3 = x
(ays. (8) 20.50 ©) n(y2-+1) - 30-4
©3030 (D)3080
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A cube is placed in a hemisphere such that four ver-
tex lie on base of hemisphere and other four lie on
curved surface of hemisphere. If radius is'' then find
volume of cube.
Ter stare Hee var van fea aR vie
eT AK TA a GaN PSE 1 TT eSATA
i eT RS a TTT TIT
aR” BR?
Ao Ose
8R° 2V2R*
O58 Oa
r= on]
In given Diagram Diameter of circle is equal to si
‘square and centre of circle lies upon diagonal of
All smaller circle touch the bigger circle, Radius of
biggercircleis J + 1 and radii ofall small circles are
‘equal. Find area of shaded reigion.
aut cia ead pra ga 8, orca ql eT V2 4 1
semi de qa a fea aot dt eraites aera art
wail
wl)
(4-2)
(B) (1-7)
(D) (3-2)
Radius of small circle are equal to r, Find area of
shaded reigion,
wat de qi at fra drome ear age ae |
(A) nx? ~ 631? ‘\
(8) Zax? - 63x?
) Bx? ~ 6 V3r*
(D) Sar’ -&
Radius of each circle =r
STA! Ratio
AA,A,A,:AB,B,B,: ACCC, =?
AAA are centres of circles (TH x8)
3, are lie on circumference (aff feat ® 1)
ACCC, CC, Care tangents (ar ar erat)
(a) 4:(2+ 98) s4(¥8 +1)"
(8) 2:3(2+ v3) 34(v8 +1)"
(©) 3:(2+ 8) 4(v3 +1)"
(0) 3:2(2+ V8) 52(v3 +1)"
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wi. G
3
Ina circle of radius 5 cm. ABand MN are Diameter
and perpendicular to each other
CG | ABand DF | MN
AE: EB=1:2=NL:LM
Find DH =?
wea fara fea 5 eh AB ake MN-=re tah oe
we at
CG | ABand DF 1 MN
AE: EB=1:2=NL:LM
DH aa aifare!
1
a 2+
O22
102.
equal to twice of nut
1
height of cone “sradits of cylinder = 3 height of cyl
inder
Ifheight of cylinder is equal to" cm then find maxi-
‘mum number of cones.
ee rar a Fe 7 ca & fer Frere ae TI
sent ate isiget at deren dere Te
a
veg St fre - vig at Sea - dere fe
oat
carrer a Sard 4 oh 8 a vegeta afiear son A,
‘eri?
(A)32,
x2
ara
wu
(43
103. Four sphere of equal Radius place on a flat table top
and touching eachother such that their centres make
4a square of side 20 cm. An another sphere of same
radius placed on them without disturbing their order
then find height of center of Sth sphere from flat top
table surface,
care war aa fae a ited at wee Art at ete ate Te ea
WaR val rat # fe Sas Hei Frey a 20cm STAT
rat arn oa Ue ise te Hy, Fae Pe a set
arc Sa 8, a a wet fer ere foes ce eT
aise tad hae ae ahha a ae See a
(A) 10(v2-1) () x
(Q10(V2 +1) 22-10
ular sect -
104.
AB=BC=3.5cm.
DE=2em
A B
D Et
(A) 6.125 (7:15
(8.125 (09.125
105. Two wheels of radii 40 cm and 30 cm. a string is
rounded around their periphery according to diagram.
Find length of string.
1 afta fara fea 40 at site 30 at Be oH ee aT
‘atten wien &, cat ah rend ara Ft
a0, 2 7
A B
Find the area of the shaded region ifside of square is
‘12cmand both AC and BD are arc ofa circleand AC
the diagonal of square.
oraifaea amt ar dave aia Fifer, afe aed at Ya 12 cm
ar AC ait BD amr sik AC faa
(A) 42.325, (8) 35.424
(©) 58.734 (D) 46.123
121,
side of the squat ‘cm, then find argajof the
a
) 510.725
) 525.625
field of Length '20’ mand breath
F aGoat is tied with a Rope of length
id the area which is ungrazed.
are & ar format cad 20 sik there 7
CESS aa 7/2 m Hee sie Te
a frat ten a dare aaa
(ayes (8) 4ay2
(ous (7
123. P. Q
T
PORS is a square of sides 2cm & ST = 2.cm, Also,
PT=RT. What is the area of APST?
PORS wr 2th. pareret ST = 22h ewe PT= RTI
PST arr Te?
(A)? (B) gem?
1L
(© V2 cm* OB
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124.
>
Find the area of shaded portion in the following fig-
ure?
‘woraifare sm er errr ar Ta?
31 22
wy o>
128,
126.
If radius of quadrant circle is '4' cm then find
area of shaded region.
aq grave a Prat '4' om tat ora eran aT
(A) (Sx ~ 2)
al)
(B) (7n- 2)
o(F>)
127. A cone is cut parallel to its base in such a way
that height of the two parts is same. Find the
ratio of volume of these two parts.
am aig a Sa ome ATI Fa WaT eT aH fr
Sei feria Sard aa @, ar feet & orearii n orTTT
wae
(a) (8)
(c) (PD)
128. A cone is cut parallel to its base in such a way
that the height of each part (1 be is same.
Find the ratio of volume of th
Trig ee omc rere eee
ren sree fe at Sra a
aa wat
129. in such a way
1
smaller cone is 755
ind the height of smaller
‘40 em above the base.
a0 % FARIRR Fe WER TET TT fe
vig ren a8 vig ores at hs ta ap
sara 40 Bet eae ah aE vig a Se a
a) 8)
(c) (D)
In a given figure three semi circles are given,
If BC = 6 cm and BD = 63 cm then find the
area of shaded region.
(a) 120 (B)or
(C)27% (D) 28x.
181. In following figure PQRS is the diameter of the
circle having radius 6 cm. PQ, QR, RS have
equal lengths. Semi circles are drawn having
diameter PQ and QS. Find out the perimeter of
darken area?
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133.
134,
135.
Mother's weaie afera + aififet
Ate Fe egg sega PQRS aoe eae Fares Feat
6 AE PQ, OR sit RS A cada aeTaR z | PQ SILOS
oer are ake ete & | rae aa oa fra 2
(A) 12 em. (B) 14xcm.
(©) 16x cm. (D) 18x.em.
The sum of diagonals of a rhombus is 10 m.
and it’s area is 9 m. What is the sum of square
of its diagonal?
TR aragys & faat st rad ara 10 a ¢ sie TaaT
Seamer 9 ath #1 el crea 3 eel ana evra 8 2
(a) 36 em? (B) 64 em
(C) 80 cm? (D) 100 cm#
Atant is formed by aright circular cylinder and
a right circular cone. The height of the tafit
4x m. where as the height of the cylinder’
1m. the diameter of both. i
is 8x m, What is the co
Acylinder, wi
a rectangle
x/6 with
cylinder.
eae Wed Ps ae Oe ora a fares Te
‘fore forrci at rand 4x @ site ae one & ara 6 FT
aro are & se ae Ta frat?
(a) or? (B) 182
(©) 36° (D) 72%
108 m.' water is filled in cuboid tank of 6 m.
side. If other cuboid of 3 m. side, is placed in it
& dipped fully in it then what is the rise in the
level of water?
ott yan aa us aia Fe 8 108 wat we ae ae
2a rar Ue Sr ra OF eT Te eT
soy, ae Seer a ia: Fras a se?
latetal surface is formed with
sonal 4r, makes an angle of
What is the volume of the
2 3
@) Emp ) > mrt
(im r. Dy 3 m. [tt
136. What is time taken to empty a cuboid with a
speed of 45 liter/min, where length of cubuoid
is 10 m., width is 9 m. and depth is 3m.
45 Chit wa 10 oi cea, 9 i hee st 3 i TeME
eA Se aT a a HTH ee eT TT?
(A) 100 hours (B) 90 hours
(©) 80 hours (D)60 hours
A brick of 5 cm height
‘wheel. The horizontal dis
137.
x x
oF OF
A solid metallic cube of side ‘a’ is melted and
from it a sphere of radius ‘’ is made. Then
which one of the statement is correct ?
sparen ede afer a a rere a rae eA
ae Fare aren & | Freetia Ha aaa eh 7
rol 1rl
Wag Bas
1 r.3 ro3
Osa OG
140. If the radius of base of a right circular cylinder
is halfed & height remains constant. Then what
is the ratio of volumes of this cylinder to the
original one ?
cafe we erergeta ters % sre a fae seit a at ore
ste sae vines ah ater ven ny, Aaa Fer a eA
cae Sera ger are orga 17
(A) 1:2 (B) 1:3
(isa (2:5
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141. A conical can whose base radius and slant height
is 3 mand 6 cm respectively and there is some
water in can, when a solid sphere, whose ra-
dius is 1 em placed inside, water just covers the
sphere. Then find the volume of water in the
can before the sphere was put is—
‘et sear aes sa ee si fees Sa ae: 3 cm.
oho om trai ge wh sagt wae | cm eT
tien sen oe awe aa raat eee a ee Te aT
aifary fe ten ere eet a aera oT?
(A) B)
(c) (D)
142.
If the internal angle of a polygon is 7/6 times
than that of a Hexagon. Then what is the
number of sides in that polygon ? :
cafe fred ary aU oral: 3m fre ae oH
aT 7/6 THU AH wp ee Te?
(Bs
(D) 10
(ay7
(9
143,
144, A circle ‘C’ is havi
is ‘O°. what is 1
circle ‘C’ and
angle of 80° ‘centre.
35 Ost Prem 6 teh, ara eR Cae Pra a TTC
Seber ar OK BOP aT orate RT AA CF FTES
eared anon?
(A) 26x cm? (B) 16m cm.?
(C) 28m em (D) 30nem.*
145. A
oo
ABC we aig @, forest fara at cen Sea h She
ea fiery ae ferret aon ‘a’ Se @, at a sr a aI a?
146.
147,
149.
150.
2th 2th
her ®) nrar
2th rh,
ae Ope
In a parallelogram PQRS, the included angle
formed by PQ & QR is 150° and perpendicular
distance b/w these parallel sides PQ and SR is
20 cm. Then what is the length of RQ ?
em Tara age PORS HH TST ST
pH a ae afar 150
(B) (w-2)x"/2
(D) (x- 2)87/4
.a of aa right angled isosceles triangle
.? What is the length of its hypotenuse?
-aetita argorg Pays wt ore 72 Se BITE
aot ah cet fart 7
(A) 6V2 cm.
(©) 12,2 em.
‘The width of a rectanglar field is half of it’s
lenght. It is surrounded by a ‘x’ meter fance.
What is the area of this rectangular field ?
Ue aaa a Ht ter saat ran St amet 2 si aE
xii ora arg gra afte & 1a a a Stat Pare?
(ay/2 m2 (B) 2x m2
(C) 2x/9 m2 (D) 7/18 m2
(B) 12cm.
(D) 24cm.
‘The sides of a cuboid is in the ratio of 1: 2:4
and it’s volume is equal to the volume of a cube.
What is the ratio of diagonals of these cubaiod,
cube,
op mremies wear weer Pet ap 2 2 4
saaa 4 8, siren we ora aR BH
eee Ta ME ew er te =
saya eat?
(A) J125, (B) Va75,
(©) v2 (D) 35.
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151. Iflenght of arectangle is increased by 10% and.
area remains constant than by what value it’s
width is decreased?
cafe ur sia Ft era 10% AER ome ak saa TET
sraftattia var ore, at sere herd Ff freee fares at eet
amet?
100 100,
a ae
(C) 9% (D) 10%
152. The diameter of a right circular cylinder is
equal to its height. Ifa sphere's of max volume
is cut from its and the remaining part is melted.
Then from this melted part an another spher
‘S,’ is made. What is the ratio of radiee of these
spehre § and §,
Te ag ha eg Sera aaa aera Sa TE
Sree aes 8 cafe eva dra the $a TT
He weed ay aera UH oa Se en §, ATT HT
Sits, 3 Presi orga sat?
(ay 22 wea
ore
153.
184,
‘area of sphere is AThen which is
correct:—
ce art ah ap we The aH fen a ara eae wt oT
er TA ara er eT en stk Fa Te Fa TS
area S% da Ho Fee te a PSs TT A
‘frafefan a a saa oH wet e?
(ayA=38 (B)A=28
(ass (D)A
165.
2N2
Ope OBB
166. A chord of a circle is of 24 cm. lenght and is 5
cm. form its centre. Then the lenth of it’s
diameter is:—
WH aR He As Ae a Ae eas ga A ew
‘cea 24 toh Riga Ae?
(A) 26 em. / (8) 24 om. /*4,
(©) 13 em./24, (D) 12. cm. 24.
167. A rectangular cardboard is of 18cm. length and
10 em. width 4 em. radius quater circles are
cut from. all four edges of this cardboard. Then
perimeter of the remaning part is (approx)—
em simran rats 19 SA, « 10S, STATE aT TA
ear eS 4 Beh, Sear gee qe ae Ty Eb aT
vt fees Cornet) Fr #2
(a) 47.1 om. /37f.
(©) 51.0 em. /34.
(8) 49.1 6m./3h
(0) 53.0 cm. fim.
168. A cirlce of maximum area is cut from a square
sheet. Then the are of remaning part is—
op ae ae 8, SRR EAT ST TI AT
“ara, re on ar rea?
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(A) 1/4 times the area of circle
qu bare 1/4 Oe |
(B) 1/4 times the area of square
wit dares 1/4948
{C) less then 1/4 times the area of square
wit arr 1/49 HEL
(D) 1/4 times the area of square
aie aren 1/4 Fae
169. The external and internal radius of a solid
metallic sphere are 2 cm. and 1 cm
respectively. If it is melted to make a solid
sphere then what is the radius of this sphere?
“eer shh rere oar fe sem 2 th
1h, & rae Paw he ren A fe Fear Te,
athe ah fee eh?
(a) 7 em. ft (Bo emma
(7 emir. (D)3 cm,
170. The radius of two taps t, and t, is in ratio 2g 1
water is flowing at the same speed from
the tapes. Two pots of similar size are
under the tapes t, and
of time filling these po
If Area of QFCE = 20
‘Area of DRF = 3
Area of PBE = 2
Find out area of shaded region ?
cafe QFCE Fe = 20
DREW ar
PBE @ @79 = 2
ah erates am a are aa we?
(ay 25 (B)23
(c) 20 (D)15
172. A solid sphere of maximum possible volume is
dropped into a cylinder jar whose radius is ‘a’
and water is filled to a heigh of 2a’. The solid
sphere is wet fully than what is the height of
the cylinderical jar such that water is not comes
out of it ?
afar Be TT TEN ME ren, 2a Se ee
Sk ge aera ar frat fe a BA fro fee ma HT
wee sr ara ae a oars Sree enh Te PE
@
ap
as 8s
173. Water is filled in a cylin
height. A solid sphere
helf to it’s height.
wae anit Sand oe SoM
raises 3/4 times to it’s height.
ren saat Sad & 3/4 aT so
raises equal to it’s height
vat San wa so
water comes out of the cylinder.
‘are 1 TET
174. A cone of 5 cm. height and 20 cm. diameter of
base is melted to make a sphere of radius 5
cm. Then what is the volume of remaining part
of the cone ?
Sieh, Sard a 20 Beh, nerds one ad vig A ferret
se fear aren wa sre area aren @ 1B rg a ATTA
”
(a) 20me
(C) nem?
(c)
©)
(B) Sem
(jo
175. A circle is inscribed in a equilateral triangle of
having side ‘a’ cm. Then find the area of the
square that is inscribed in the incircle?
Tem Ta a ps ara we Pope A sins 1 sa art aT
apna art Shea sia a sinc 87
a a a a
“OF BF OF OF
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176. If a prism has base as right angle triangle in
which side 10cm and 12cm make 90° angle. If
the height of prism is 20cm. The density of
prism is 6 gram/cm’. Find the weight of prism.
fara ore wee an Pn Fre 90° alors ap
10 ae, oft 12 Att, & Heer at Sa 20 ah. @ fem
Sra Ts 6 UVa @ ot ee aT a aT TT
(A) 6.4 kg/ fret
(B)7.2 kg/ Feet
(C) 3.4 kg/ faci
(D) 4.8 ka/ Pech
A prism made an a square the height of prism
is 15cm and the total surface area of prism 608
‘cm? find the volume of prism ?
fre cian orem aa few ai Sard 15 ah, Bate
an ga yeahs Stave 608 Se # at fae a see aT
wt
177.
(A) 408 cm? (B) 460 cm
(C) 1500 cm® (D) 960 cm*
178. Three cubes of a metal having sides 6 cm.
em. and 10 em. respectiv
new cube is formed. The
the new cube is ?
os at
iz,
woe
(a) 10
(C) 16 ¢3
179. The perimeter of is 12 mt. more than
the perimeter of Ifthe area of S, is 11
less than 3 times the area of S,, then the
perimeter of S}i8 >
ward S, after, ant S, a afeea a 12 oF, afer ae
$, saree, 5, area a TAA 1 we, aS,
ferent?
(a) 24 (B)32
(C) 36 (D)40
180. A prism of a triangle whose perimeter is 28 em
and its internal radius 4 cm. If the volume of
prism is 336 cm’, Find the height of prism?
Ur fsa a ore 28 Soft afters aren we Pt fare
sia Free 4 ah, ate fro ae rea 336 Ba! a
aie a San aT
(aye
(4
8
(D) 22
181.
182.
184,
185.
B
Ke
7 e
Find out Area of Circle ?
aan dae aaa?
16
(A) 317 (8) gi*
A cylinder is formed a le
from two
d cylind:
ama 5
oe era ar oat 7
‘curved surface area will be ?
areata egal Fema aa a oe fal Seals
Deora, dae am gaia deat segura?
(Ao:4 (B) v3:V2
(c)3:2 (D)2:3
‘A cone having 3 cm. base radius and 4 cm.
height is cut down from a solid cylinder of radius
3 cm. and height 4 cm. The volume of the
remaining solid is
4 tht, Sar sit 3, fer ara de en Fa os
eh. Set ates ah, orem fae at aia fea ae a
‘omc § B18 yu ater a arate #2
(A) 9x em? (B) 15n.cm2
(©) 21n ems (D) 24m em.*
A conical flask having base radius ‘r’ and
height ‘h’ is filled with milk, this is poured
into a cylindrical faske having radius 2r. The
height to which the milk rises in this flask ?
ree fen Sr een we rae a Ge
see 8 2 Bera ere were Se
‘aren 8m waren Hg Pert Sr ae som?
at of
of os
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186. From a cyclindercal wooden portion whose
hight and diameter is equal, a sphere is cut
down of maximum volume. Waht is the ratio
of used wood and unused wood ?
ers Be rare ame B fre oaTH Sera Soar aR
aera mera sr I we Terre Be FHT TAT
tari F om are & seen oH Ae aT
are ene we orga ?
(ay 2:1 (By 1:2
(2:3 (D) 3:2
187. A semi circle ring of 8 cm. diameter and 2 cm.
thickness is melted. How many small sphere
can be made out of it having 2.5 mm diameter?
8 ii, one sk 2 Sail, Sten ae sraquta apa aT TTT
‘fect seen Hi 2.5 fr, are a feral ra oH aE
(ayo1a4 (B) 3072
(©) 1536 (D) 768
188. If the metamal permeter of a hemi-spheral bowl
is 132/7 cm. then is capatcity is ?
afe we statics ak & sarattm a a ofa 13277
wh. @, deat fear ere?
(A) 120 cm. (B) 18x cm.*
(C) 24x em D) 36x c1
189. 9
of the semicircle ?
ai, ae a rz A ea
ma?
4 8
5 5
or ms
190. If h, c, v are height suface area and volume
respecticly the the value of Snvh® = c’h? + 9v?
is?
“acho, wR a vig a See, Te A en ATT
8 wa imb— che + eT AE?
(ayo @yt
(2 (D3
191. If the area of the incircle in the equilatral
triangle is 4x om.%, then area of triangle is ?
a we eg aye rene der = TH.
fran dora ea?
(A) 123 ems (B) 93 cms
(C) 8V3 cms (D) 18 cm*
192, A 8
5 6
i vearral @ | AEFC wr tm sera are 7,
TR Pa vee ras HI faeoh AC ten eae AT
ret area ora D wea IERT ABCD % tae
Hae AFC & ataeet a seq FTE?
(a2 (B)3/2
(ce) (D) 8/9
193. The length and width of a fiedl are 125 mt and
15 mt respectvely A pit 10 mt. 7.5 mt. » 6 mt.
is dug from the field and the mud is spread over
the remaining field uniformly. The height of
the field rises by ?
wer ea at ea 125 af. oem ste 15 Hh ET TH 10
7.5 Af, x 6 oh er Teer eter en sik Tea rnc fea
rare Ge oo es wa then fea we fete
& fra eee aa ar Ta Soa A aT?
(a) 15 cm. (B) 20 cm.
(©) 25 em. (D) 30 em.
194. What is the total surface area of the cubical
box which is opened from one side whose outer
side is 5 cm. and thickness is 0.5 cm.?
SER or aA qe ae a AE ys avec Te,
‘forest aera Bt ea 5 Het, Ten stare 0.5 Sei. e 7
(a) 125 m2 (B) 214 em?
(C) 180 cm? (D) 205 cm+
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195. A solid cubical stucture having side 4 cm. is
melted to from solid cubes of 1 em, each. If the
surface area of the melted cube is x and the
total surface area of the newly formed cubes is
y, then x : y will be
URE afer ate, Foe yar ah, a me
ef, ee sare herr a ae ere a dt
yo dorm x &, stoame me ash ate age TS Soe
yt atx: yant?
(aya: (1:2
(1:4 (4it
196. If the measurement of a rectangular box is in
2:3: 4 ratio. The difference between moulding
the metal sheet at Rs. 8 per sq, mtr. and Rs. 10,
per sq, mtr. is Rs, 234. The length. width and
height of the box are ?
a ora a a fad 2:3 24th orga & ea 8
a wna ster a aca 10%, afar seca ea Pet
siga anata a sphtamas ata 234% eRe
ve cand, vere a Seo oe 8?
(A) 2mt.,3 mt, 4mt. (B) Smt., 4.5 mt, 6 mt
(C)4 mt, 6 mt, 8 mt.
197. The ratio of radius and hei
(A) 24m
(C) 48x
198, The biggest solid
of side 3 mt. Volume of the ramaining solid is?
we th at oad a oe aaa aa oe
sire rae Ferrer fee aren 1-8 Sen ETAT
*
(A) (27-2.25n) m2 (B) (27-4.5n) ms
(C) 2.25n m2 (D) 4.25% m.?
3
202.
original circular shape. Find the ratio of origi-
nal paper to remaining paper. The radius of
small circle is 1 cm and radius of quadrant 5
fre queer a at sa cae a set # ae aT
raring 28 # ae Feorge oaae at &, Faa eat
1 deh ven a8 ga at fens ath 8 aa are et
sree 4 aren ort a areafers tex cen oe te & aor
rT ae A
(a) 25:16 (8) 2549
(0)20:9 ON
In the given figure a rectn: pint
Pand E are joins respective
he area of shad mn. Where
cm’, 3
(B15
{D) None
Water is filled in a conical flask of height h.
‘This water is poured in a cyclindrical flask of
same height and same top area. The new height
of water is ?
h Sead & visser aa A art wea gon 8 za ae at set
Sag ven set itt dearer area Sera aes F fra fea
rat & art ay eR a Soe BP
2 1 2
5h Gh Fh Eh
A 5.5 om, side solid cube is put inside a
cylindrical 4 tensil partially filled with water.
199. ‘The diameter of 4 tensil is 11 mt. Ifthe cube is
completly submerged in water then the height
to which water rises ?
8.5 ah, or are we Ste a a ee Saar wT A re a
ge aera aka ren fea ae aa a 11 He
trae a yt ae sem a oe, ath aT eR
A circular paper is folded along its diameter | seu?
then again itis folded to form a quadrant. Then (A) 3.75 cm. (B)0.75 em.
it is cut as shown in figure and reopend in the (©) 1.75 em. () 2.85 em
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208. C, is a right circular cone whose base radius is
rem. and height is h, em. and C, is right
circular cylinder whose base radius is r, cm.
and height is h, em. If, :r,= 1: n and both
have same volume, then which one of the
following is correct ?
Ctr errr aig &, feet ere fea 1, ah ai
Sa h, Fi. & ait C, wR craga-aR Aer @, forrat
orem fae r, site Sarg hy He, @ ave r,s, = Len wen
Ter we quiet) otters ora aarti, at Prat
aa aeE eae?
(a) h, = Sn, (B)h, = seh,
(Qh, = 3n, (Dh, = nh,
A right circular cone is cut parallel to its base,
such that the oirginal cone and the newly
formed smaller cone have their slant height
in 2: 1 ratio. If v, and v, an the volume if
204.
original cone and newly formed cone
respectively then v, : v, is ?
“em ETT ep SA SMT He A WH Te BLT
Wa Fre rene fae et veep athe ee WER eT
ig a fen Soba 2 a eT AAR V,
Vit brah
ree ce a
(A) 2640 em. (B) 2604 cm.”
(©) 2460 (D) None of these
A spherical ball is placed our a right circular
cylinder. The radius of sphercal ball and
cylinder is same, ic 15 cm. If the volume of
ball is 32400x cm.’ then which one of the
following will satisty the height of the ball
UR Ta UR aE a SUS Hers & TET AT
vitor at fre ote tera ara toh a5 a
21a wa Farr 324000, @, Gh oa at Sea
Fara 8 a ats 8 we at age wet?
(A) 135 em. < h < 150 em.
(B) 140 cm. 50cm?
219. A road roller, whose diameter is 70 cm. and
length 2m. is rolling on the earth. than find
out the distance travelled by it in SO rotations?
1p te, Famer aaa 70 She rene 2, 8, get we
ces fa aaa 8 Se 50 Tea A oa TTT ya
fern’?
(A) 180 m2 (B) 200 m2
(©) 220 m2 (D) 240 m2
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220. A cyclindrical rod of height h is disolved and
convested into cone, whose base radiusis twice
to base radius of cylinder ? find out the height,
ofcone ?
WR h cred a aera wy a Tere oe E sik A eR A
wen sm & faerat soar fen Aer et Tar fT eT
apie ig sts fers?
(A) 3h/4 (B) 4h/3
(©)2h (Dyn/2
221. A cyclindrical pot having base radius 14 cm. is
filled with water to same height if a rectangula
solid is dipped in it with dimesions 24 cm. «7
cm. * 5 em. then find the increment in water
level ?
We aera Wa Hy, forest aa fae 14 et 2, TT
ge Sea oe va are ate 22 A «7 a x 5 A
Frm a ee sree dhe saa gare seer e, at ae
ac fare af eet?
(a) 0.5 cm. (B) 10cm,
(C) 1.25 em. (D) 1.5m.
222. A pencil is a cyclindrial lead. The length ofthe
pencil is 21 cm, and raidus 0.4 em. an¢
223. The
radius of
fret aig oh gM fren ai om ee: § cm ae 25
cm 813 an Set ome one wT
a FoR aT STITT 110 em? t, Ta BE vig aH Prem TT
al
@ 8
© ©
224, A container have as much paint, which is
sufficient to paint 5.875 m.* area. How many
bricks can be painted with that paint of
dimensions 12.5 em. x 10 em. * 7.5 em.
Top Para a He 8 5.975 Hh eR Sone
are ach fee vata em ea 12.5 Beh, 10a +
7.5 fh, Pam eh Prt He at a?
(a)225 (@) 180
{c) 150 (D) 100
225. The ratio of the volumes of two cones is 4: 5
and the ratio of their base radius is 2: 5 then
find out the ratio of their slant height ?
a sigei & ovat ar organ 4: 5 ¢ sit saat oman
feast moun 3 ¢ ret wai Saed aoa
ame?
fA) 5:6 (B)6:5,
(9:5 (D)5:9
A right angle triangle having sides 5 cm., 12
cm. and 13 cm. the triangle self rotates at 12
cm. side so find out the volue of such formed
solid ?
ep rai ngs Fara pad Sf, 12 13h,
aE 2h ah pT a:
say he rae aT?
2 and
then how
pipe in 1 minute ?
(B) 15 liter
(D) 1.5 titer
in the form of a circle having radius
m. If it converts into a square them find
out the side of the square ?
Um a 42 ae, feat ae Ta Ae aie sa eH
ora a Ste sez, at sa at BT TST Pat ert?
(A) 66 cm. (B) 42 cm.
(C) 36 cm. (D) 33 cm.
Seven semicircles ane removed from the
rectangle ABCD as shown in figure AB = 2
cm.and AD = 0.5 em. are given. If the radius of
each semicircle r, 5, t, u, Vv is half of the radius
of the semicircle P or Q. find out the area of the
remaining part ?
‘ore Faeroe orga sara ABCD Aaa stale ee
Fira fear Tat | AB= 274. sik AD =0.5 Sh. BHR
rT 1, 5, tu, v9 Baoan area pg warn MAE
get ye ur mr Staewel ee?
A 8
D sD q
ce
° €
(A) (128 13n)/128 em2
(B) (125 ~ 13n)/125 em?
(©) (128 - 13n)/125 em?
(D) None of these
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230. If height and base radius of aright circular cone | 286. A solid cone having height 8 em. and base radius
is incresed by 20% then find out the 6 cm. is melted to form smaller equal even cones
approximate increse in the volume ? having base radius 1 cm. and height 2 cm. The
ale wen et vipat ser Fae st SH 200 number of so formed cones is—
Shon, ase sare A tree fer af eH ert? Sar 3 ai. otk sar fear 6 Ae, at eH Sta aig FT
(a) 60 (B) 68 frre Sa were ara ear 1 ae, si Sa 2 aH. are
(73 (D)75 cater vipat 8: aren arene tia ipa a seo ee?
231. The radius of base of a cylinder is 2 m. & it’s (A) 36 (B)72
altitude is 3 m. What is the length of it’s (c)144 () 180
ise tena caer 237. Side of squre ABCD is 7 em. then find out the
vee er ae a fe 2H, & ate sera sini 3 ey
1a seit He (section) % farsi a cA Fae 7 .
(a) 4 mat. (8) 5 mat. a ee Bic FATA
(©) 2.5 matt. (D) VB mrt ae a BO ora Fis
232, How many liters of water can be filled in a i
hemispherical pot having radius of 21 cm.
em te Trew a Hy, foreat fae 21 Sh & feet cer,
‘wet (orem) ara?
(A) 19.4 liter (B) 38.8 liter
(C) 194 liter (D) 388 liter
233.
(B) 28 ems
) 14 em? (D) 21 em?
238.
234,
Hil a2, er wer? are fare few i fae so Beit é bate 7 figure all circk aa
—— In given figure all circles are in an equilater:
: Es S pada s we hale a eo triangle and radius of each circle is 20 em then.
coe ate ocean find the perimeter of triangle.
() 30 (D) 35 u
235. A cyclinder cone having internal diameter is (a) 40 (2+ V3) em (8) 80(2+ V3) em
filled with water A solid sphere of radius 6 cm.
is dipped completely in the water then what is (€) 120(2+V3) em (D) None
the increase in the level of water ?
We aera TA (4) Hi, fares stat are 24 Hat 2, wt | 239. Volume of a cone is equal to the volume of a
$1 ee 6 Sh, cer ed dea ae ae a sphere if the diameter of the base of cone is
fant gh? equal to the diameter of sphere, then what is
ivan : oe era ne " a the ratio of height of the cone to the diameter
of the sphere ?
(C) 2m. (D)3cm,
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241.
242.
243,
Mother's weaie afera + aififet
244. A hemisphere is made up of 1 cm. thick
ep opr are ee rR SPT IG
Somat arene Ha ore TRE, ap STE
sitet ie oar ee seq?
(ay2z1 (By:
(3:1 (Dart
Arhombus and a retangle having equal height
are standing on the same side and on same
base. Ifthe perimeter of rhombus and rectangel
are |, and l, respectively then which fo the
following is true.
saa Ser ears ote ere ow A TE ate
rer or A es ae # ae a She oT
fear me, she 1, a eae 8 aa em at
a
(aici, it
(i> i Buri e2, (Dh = 24,
A right circular conical bowl is made of a semi
circular sheet having diameter of 28 cm. What
will be the capacity of the bowl.
29 Sh Sara ag aft orga eft ee = He
faga ease Care Tar wes | sa aT a ata
(A) =—V3 om? (B) 3003
oes
Aculj Ose
hei s. If
their 1egatio of volume
of tote
a ‘ear ra feet
Saige ‘een ome wart tg
‘frm a ee Be ore TOT Te |
4 5
(3 @
5 8
oF OF
A bowl having internal radius 20 cm. is filled
with sause. That sause will be filled in bottles
having radius 5 cm. and heiht 8 cm. Give
required no. of bottles ?
207, siratee fan spines wait Faia sa ais aT
Sart, fret ak 8 ai. Sere ret waareR ateeit A rT
Bl smaeae Staci Bt ea Tz?
(a) 100 (B)90
(©) 80 (D)75
mettalic sheet If the external raidus is 5 em.
then find the weight of the hemisphere (1 cm.’
mettalic shat have 9 gm. weight.)
1 ah shag at arce Bw seston ere eT ae
ara re 5 Sh &, ah arti om ome a8 7 C0? oe
ara ume)
(A) 54x. gm (B) 366n. gm
(©) 122n gm (D) 108x gm
A sphere and a cube have.same surface area.
what will be the ratio of
of sphere to the square of
radius of a 7 m. long
pipe are 2 em. and 4
‘fread aa: 2 ah, ott 4 at. # ale 1000 AH?
cara fem, ah eft oe a ee?
(A) 264 kg, (B) 182 kg.
(C) 396 Kg. (D) None of these
Their is a circular plate of area A,. A circular
plate of area A, is cut from it assuming it’s
radius as diameter. The remaining area is
represented by A,, then—
area Aoi em RT a a OE zee Fae a ea
rea uA, Sara a we gar a A, eH a are a
‘avdh 81 Sra wert dear A, are eta &, a:
(A) Aa, <164
(0) AA, =2685
(B) AA, > 16a;
(D) AA, > 283
What is the area of the largest triangle drawn
in a semi circle having radius R ?
fren Rand wn arte ai meat a ae ap ae
*
(ayor® (By Re
(FR Dae
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Direction (Q. 249.-251):— Assum that the two cet AerareR ave a, fret fe seat Sood sh oe
Sap St fru Sere @, Frere Ser FH fae aR Pea are TT
Pine oe ele lee ee ne ‘ane ret re | eareaTe ateat at eet Te?
frau fr tft Sed ae? (2 @3
(A) 3y20 cm. (B) 610 cm. (4 (D)s
(C) 12 cm. (D) 15 em, 255. Internal & external radius of a cylindrical pipe
250. Find the height of the cone ? are 4 cm. & 6 cm.. If its length is 10 em. then
vega Seri oe? rat wil be tinal stan oxen te Die
(A)9 cm. (8) 12 cm. pear set are aie arate ae ore: 6 Zh ag
(C) 13.5 om. (D) 18 em. Seth vafeguet cen wah
251. What is the total surface area of a given. Beier F fer?
frustum ?
fog amy fers sep ps rect ene?
(A) 9x(2VI0+5) cm? (B) 9n(3VI0+5) cm2 | 256.
(©) 9x(3VI0-+4)em2— (D) 27m(3VI0-+4) em:
252. In the given figure AABC is right angle triangle
where B is right angle, BC = 21 cm and AB= 2
cm. A semi-circle whose diameter is AC an greater than the area of
‘quarter circle whove radiusje BC is drawn Srv, whe aro ara
find the area of shaded portion. fe circle is less then the area of
square. /FV7m aH, ate Sara see
(othing can be concluded /e7H ae, 71%
Seas waz
257. What is the radius of incircle of the triangle
with sides 35 cm. 44 cm. & 75 cm.
35 Wi, 44 Sei. ait 75 Soh. cea Ft sii at
eed oraquat feet?
(a) 3 cm. (B)4 em.
(a) 425 em? (B) 425.75 em? (C) 5 om. (D)6 cm.
(C) 428 cm? (D) 428.75 em? 258. What is the maximum length of the rod that,
. can be placed inside a cuboidal box of length 30,
as tien thelarea ote cle eboee latter cm., breadth 24cm, end height 18 em ?
Seqena . Senora tino foo sores ‘wre 30 fit, cher 24 Beh, ste See 18 Hh, sare ATA
. ac wa ve crertfors sapere eer agar ee ay at arch
ee wea aaferman card ame?
(a = om? (6) % ems (A) 30 em. (B) 30V2 em.
(©) 24 om. (D) 185 em.
(¢) ems (0) % em: 259, Volume of a sphere is 8 times of the volume of
4 other sphere. What is the ratio of the surface
284, Acylindrical iron rod whose radius is one-fourth areas of the two spheres ?
ofits height is melted to recast spherical balls em a aT BE A STATA 8 THE SA TS
whose radius are equal to the radius of the feared or sega ve?
cylindrical rod. Find the number of spherical (age (Byard
balls? (02:1 (D433
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260. A rectangular area. of 6 cm.” is to be painted on
aboard of 3m x 4 m. in such away that it leaves
same area on all over the sides. What should
be the width of the edges ?
37H, <4 sh ote 6 at, Tra Be TR
ron Pe aa ai ote epee the oH eT |
fran at aed en ert ae?
(A) 0.25 m. (B) 0.5m.
(C) Lm. (D) 3m.
261. Curved surface area ofa soild cylinder. of height
9 m., is 1/3 of the total surface area. Find the
radius of the base.
ot Sree re eer Sta dere oe aT Er, FOUTS
area a Ue fren & | swan at fem fate?
(a9 m. (B) 18m.
(C)27 m. (D) 30 m.
262. A big cylindrical tank, Which is open at one end,
is half filled with water. similar solid sphere
are to be placed into the water without splitting
the water. If height & radius of the cylinde:
equal and are 4 times of the radius of
sphere then what will be the maxini
number of sphere thatean be placed
(C36
268. Radii of two cifeles are 18 cm. & 8 cm. Distance
between centres is 13 cm. find the
number mon tangents ?
Aaa S ore 13 eh. sik 8 et. Fre eT at ST
Fi 13 Sh. @ mets wre ensil at een fret é ?
(ay 1 (B)2
3 (D) None of these
264. If height of a cone is increased by 50% then.
‘What will be the perecentage increases in the
volume of that cone ?
cafe fare vig at Sree sox age on 2, oh aig oT
‘ferent ferera afe Bt et & 2
ae (B)40
(50 ©
265. Three cubical biscuits each of dimensions 0.3
m, 0.4 m & 0.5m. are melted to reform a new.
cubical biscuit. Then what will be the total
surface area of the new cubical biscuit ?
cafe ata ara foepal a, frvis ae aM: 03 Hh, 0.4
0.5 HA. Foe she ona a Pepe a &,
seta free as hawt a?
(a) 1.08 m2 (B) 1.56 m2
(C) 1.84 m2 (D) 2.16 m2
Internal radius é& thickness of the wheel of a
eycle are 50 cm. and 10 om. respectively. If it
revolves 10 cycles in 5 sdeends, 3d the
speed of the cycle ?
(B)8.cm,
(D)6 cm.
A frustum whose height is 8cm and lateral
height 10cm. Find the difference between
upper and lower base radius is ?
er fore foraat Sra 8 ari, cen et eas 10 ae.
at set sat cen Fractt feansit om ste ar eT |
(A)6 em (B)4em
(C) 10 cm (D) 12 em
269. The radius of the circular ends of a bucket of
height 15cm and radius of upper circle is 14cm.
Find the radius of lower part if the capacity of
bucket is 5390 cm’.
fare foran aed af Sard 15 ah. 8 ven att ae BT
‘from 14 tnt, tga gre 9390 Se ort on wee aT
‘fract ae at fen aa vfs
(a)7em (B) 21cm
(C) 8m
(D) None of these =r 8 ate 78
270. What is the volume of the sphere whose
internal and external diameter are 8 cm. and
10 cm, respectively ?
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aa tet iret an saat (Ah? H) ant fare safes
st ara ars HAT: 8 A, site 10 A. aT?
271. Suppose, earth is the sphere of radius R. so what
will be the radius fo the circle at 40° S
ongitude?
sa ify, yo R Fae ten 1 40°S seat ea
fren?
(A) Rcos40" (B) Rsinao*
(C) Rsingo" (0) Rtan4o"
272. The length of the diogonal ofa rhombus are 55
cm and 48 cm. If the perpendicular height of
rhombus is P. then which of the following is
correct ?
wep aeagis 2 frail at tal ss ah, she a8 Ah
Safe saeqiis at cea Sad P
wrap ait?
(a) 36 cm. < P