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411 views67 pagesMG Mensuration Questions
Mensuration question
Uploaded by
Kumar GauravCopyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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/ 67
MATHS SPECIAL
a FOUNDATION BATCH
FREE E-BOOK 7-7 MATHS FOUNDATI
S
21 om from 1 ew aren, euais ae
ara &, at ame ret & oer Bi war WH ATE 1.68
am Bi aft tar gota: ga aren 8, at Te eT Fae
Feeerar soar
fa) 1.25
{e) 1.5
1
(4) 1.75
22.16 cylindrical cans each with radius 1 cm are
placed inside a wooden carton four in a row. If
cans touch adjacent cans & the walls of box
then which of the following could be internal
area of bottom of carton?
Lom Rear & 16 dearer fe ey weet & eRe
Fe Fa be ow at ait a AH dart
ert ara & ot Bret a & ete ar ere oT acts
arena ore
(a) 92
(0) 68
(c) 64
(a)16
23.A heavy sphere of maximum possible volume
in to be completely immersed into a
cylindrical jar of radius ‘a’ containing water up
to a height 2a, What is the minimum height of
jar so that no water spills out?
afer area er ater we ara at oa: EAT
(6, Brat Rear tae och & aa A St
2a Bat er er er Seg we ahh FE
art wee aT were?
{a) 109/38
(bo) 109/5
{c} 109/7
(4) 109/11
24.A right circular cone is divided into two
portions by a plane parallel to base & passing
through point which is 1/3 height from the
top. Ratio of volume of smaller cone to
remaining frustum of cone is?
oe abe YH CHT CAT AE TAHT CT
aval Ht wfer ara 6, a 1/3 Sarg we we
Fer ee Bese A araet HT TT FAT rTP
(a) 1:35
(0) 1:26
(c) 1:27
Ln f= Za
y SaaS ion, ON)
eee eee d
(a) 1:29
25.4 cone is cut by 4 planes parallel to its base
into 5 parts of equal height. If volume of
biggest cone is 375 em’, then volume of
biggest frastum =?
wer tig FT SUR & aaa 4 Stary GANT S HPT
A rer orar B ee Sous wars BL aR at ag aT
SITET 375 em? &, at a8 eT eT ara?
(a) 285 cm?
{b) 188 cm?
{c) 184 cm?
(a) 183 cm?
26.2 cm of rain has fallen on a square km of area.
50% of water was stored in a tank of
dimension 100m x 10m. Find increase in
‘water level in tank?
1 oa Prof. atewa 4 2 cm ot Bet B, 50% ot
om ten a arr Arar sre &, Fares efor? 100m x
10m ¢1 tor 3 oh & ear H ah Seng ae
Pfau)
(11m
(10m
{c) 15 m
(4) 18 m
27.The length of longest pole that can he placed
on the floor of a room is 12m & the length of
longest rod that can be placed in the room is
15m. Height of room =?
We AT & Oe afew Seng eH ET HT
aeag 12m t a eat 4 at eer A aftereer
Weng 15m 8, wat A Seng aT elt?
(a) 12m
(b) 25 m
(c) 18 m
(om
28. Two spheres of radii 6m & lem are inscribed
in a right circular cone. The bigger sphere
touches the smaller cone & also the base of
cone & smaller sphere also touches the side of
cone. Height of cone =?
Gem TT Lem fear & ct Te Ow ey A aT TT
Bag ata, whe aha et aor aT Te
amet & ae ter ater aft chy A aga et ERE aT
tig & Sat =? os (
{e) 3296 {d) 4436 20
65. A cylindrical vessel open at the top contains
water up to 1/3 of height. A heavy sphere
whose diameter equal to height of cylinder is wa
placed into vessel touching its curved surface 7 20
from all sides, then water level will be at what
height?
Uw daaPeR wet at HTB Get E, 1/3 Sug Tw
2
vet & mer BL ew att ter erence tect ft 7 »
Sang & wre b, tar ca rer fat geht att (a) 1120/7 {b) 160/7
drat ot erat ca B at rch er eae eth Serf —_(6) 180/7 faseone
ar 3da07 68.PORS is a rectangle in which side PQ = 24cm,
{a) at half level point on RS. What is
(0) at the top
{c) at 3/4 level. PQRS Uw area §, fort aaT PQ = 24cm, QR =
(4) at 3/8 level
66.n the given figure, PQRS is a square of side Léem ait 7, RS a Fear AG b APTQ AT Tw
‘8cm and 2PQO = 60°. What is area of \POQ =? TFT err?
2 7§ ampft 4, PORS er a 8 Rr AEST Bem {a) 192 (b) 162
aitt 2PQo = 60° $1 APOQ IH cota FAT BPP (e148 (@ cant det.
69.A right circular cylinder has height as 18cm &
radius 7cm. The cylinder is cut in three equal
parts (by 2 cuts parallel to base}. What is the
% inerease in total surface area?
ee TUNE ter FH SAF 18cm sy Feat Tem bh
aa) are & aia te aT dt RT
srreit A orrer rar Bi er yom eta AF Aree %
Fi avladt oh
(a) 3243 (a) 62 {b) 56
(b) 24 5-2 () 48 (as2
(c) 48 3-1 70.PQR is a triangle whose area is 180 cm?, S isa
point on QR such that PS is angle bisector of
(a) 16 3-3 ZQPR. If PQ:PR = 2:3, then what is area of
67.1n the given figure, two squares of sides 8cm APSR?
& 20cm are given. What is the area of shaded POR ew fiat § Free eT 180 cm? B 8, QR
part?
2h mf apt scm ae 20cm ct wt fem || Ree Reg gee B PF PS, cOPR a
1 wraifecr rer st ear ter? wacPeras $1 af PQ:PR = 2:3 dt APSR
ewe =?
(a) 90 (b) 108
(e144 (a) 72.
INSP. MOHIT GOYAL SIR i at ol) i er ele)
N BATCH
Chetek ade tad
MENSURATIONE:
re ee ee ed
are Bi arcertret Ft re Som B, athe why A Sars
dem bi feat 1 pa qo crea =P
(a) 75.43 (b) 103.71
fe) 85.35, (4) 120.71
If from a circular sheet of paper of radius
15cm, a sector of 144° is removed &
remaining is used to make a conical susface,
then angle at vertex will he:
ae eR PARE Fre * ors a fae Pr
1Sem §, 144° 1 UF aes Hem Prat ater Bote
at ge ner Bow igor Ta UT ah Bat
at ox war ator = 2
6
(a) sin
fb) 42,63
3
(0) don
58.)
13
(@) ein’
59. Two concentric spheres A & B have radius r &
2r respectively. A cone is inscribed in latter so
as to circumscribe the former. What is the
curved surface area of cone?
Owen te Aah BoM Peart sew: re ar Bi
Feet are A HAT Te GAT aT OF Hy TAT
sear 81 ig aay Rie var eT?
fa) Sar?
) Tar?
fe) Sar?
(4) 6xr*
.A rectangular tank 25cm long & 20cm wide
contain water to depth of Sem. A metal cube
of side 10cm is placed in tank so that one face
of cube rest on bottom of tank. Find how
many liters (minimum) of water must be
poured into tank so as to just cover the cube?
wee arraren Gey freht wearg 25cm ae wish
20cm 8, 4 Sem apg aH TKN Fa Bie 10cm
agar wr oat ten ge eR Tar rer & A oT
ew way ton & oer We BI feet aiet ot tow
Sat art Brat er Gr ye arte
{a) 3.5 Itr.
(b) 2.5 itr.
(c) 1.5 tte.
(4) 3itr.
Half of large cylindrical tank open at the top
is filled with water & identical heavy spherical
balls are dropped into tank without spilling
the water out. If radius & height of tank are
‘equal & each is four times the radius of a ball.
‘What is the maximum number of balls that
can be dropped?
ee daaren ton of oar & gar § aie ae ot
Sore bh wart ataren ae Oe at Re at ore
ort art 61 aft tar ft fren at Sears wera F
ar wet He Roa A are aa, at
‘firrt dey At sear srt ar act B1
(a) 28
(b) 24
(ce) 36
(a) 48
A square & a rhombus have same base &
thombua is inclined at 30°, "0 ap
er a atte wore er ame wat Fae
wraps oor a, SE =o
(a) 3:1
(by 1:2
(yaa
(a) 1:3
A cylinder of radiue 4.5 cm & height 12em
just fits in another cylinder completely with
their axis perpendicular. What is the radius of
second cylinder?
(ys
te) 15
16
(a) 7.5
A right circular cylinder has height 28cm &
radius of base 14cm. Two hemispheres of
radius Tem each are cut from each of two
base's cylinders. What is the total area of
remaining part?
Ue ARR Farr A Sef 28em F Ie aU Fo
Adem $1 deat yeh amet 7em frou ¥ et
aden sme ard Ft ge eT per eT FT
wre
(a) 3842 (e) 4312 La
OUNDATION BATCH
La
MENSURATIONE Za aue
eee
(b) v/4
(eh W/7
avs
49.4 hollow square shaped tube open at both
ends is made of iron. The internal square is of
Sem side & the length of tube is Bem. There is
192 cm: of iron in tube. Find its thickness.
wee arch eoteer aah at cat aie & aah B, ate AT
wang art bi arate ot Fr aor Sem B ait aah
Ft aeMs Bem 61 aR aah A193 cm! aig wT
6. at gett aterg aie Fifa
(0) 0.5 cm
@) 38cm
fe} 2em
(4) lem
50.1f a sphere of radius R is divided into four
identical parts after being polished. Ratio of
polished area to unpolished area?
aft R Pree er ew aren ifr & ae ae wat
aretha aver avert & att fever Per aera Pear
sifer Fa ard arr A atawer wT ar aT OT?
(a) 3:1
@) 1:1
fe) 12
(a) 2:1
51. The height of cone is decreased by 64% then
how much % should base radius be increased
to maintain same volum
ew tig A Song G4 Ag at Se aT
roar a Prat 96 FY agent oh, feted are
wat WP
(a) 87.5%
(b) 80.75%
{c) 66.65%
(4) 33.33%
52. The number of spherical bullets that can be
made out of a solid cube of lead whose edge
measures 44cm, each bullet being 4em in
diameter.
ew ote wer &t Fare aa Adem 6, Fret stare
Ac wart an awe 6, aie setw ERC MT CT dem
eR
fa) 2541
{c) 2514
(b) 2451
(a) 2415
53.1f surface area of sphere is 346.5 cm*, then its
radius is:
ie we aha HT GRRom eA 346.5 cm’ fat
ht Peat =?
(7,
(®) 5.25
(c) 3.25
(a9
54. Radius of base of conical tent is 12m and the
tent is 9m high. Find the cost of canvas
required to make the tent, if one square meter
of canvas cost Rs120.
om eiganen tee aru Peat 12m ate Seng
9m bee et wat A wer ee (ere) FT APT
are More A im? Herre HT APT Fe 120 Hh
(a) 67830
(b) 67800
(c) 67820
(a) 67824
55, Except for one face of cube, identical cubes
are glued through their faces of given cube. If
each of given cube measures 3cm, then what
is the total surface area of body so formed?
a GR Teg HT Ole aA Ie wa we TT
ore Oh af wet oa A eT Som b, at eh ap
oe aeyet pester err ea wT
(a) 432m?
(b) 240 om?
(c) 243 em?
(4) 234 cm?
56.If radius of cylinder is decreased by 50% &
height is increased by 50%, then % change in
volume =?
aR ww tea A From som & uel bat Serf
50% & we at sae areca ofeatet Ber?
{a) 62.5%
[b) 66.66%
(e) 75%
(a) 50%
57.A toy is in the form of cone mount
hemisphere, The radius of hemi
and height of cone is 4em. T.S.A of toy =? FOUNDATION
Ltd
BATCH
INSP. MOHIT GOYAL SIR
MENSURATION
100/119
7
179, Accube is cut into three parts by two
vertical slices. Find volume of shaded part.
ew ey Yah ea GT ART at MT HF
sper rar BL eater mer eT ete ae AAT
fa) 3,500
(@) 4,000
{ce} 3,000
(4) 3,200
180. A right circular cone & a hemisphere lie on
opposite sides of common base of 10m
diameter & cone is right angle at vertex.
cylinder is circumscribed in this position,
then what additional space will be enclosed?
Wer TER tig ate Ow aU, are ST
RAT STAT 10m BF, Revie a oe Rex Fi
WE ww tat eae ane TET ara B at Pre ate
ear tu arr
fa) 1408,
(b) 1360
fe) 126
(4) 1250
181. Given below a square OPQR of side 25cm,
two quadrants are drawn with P & Q as center.
A square inscribed between them as shown,
then aide of square STUV will be:
at es TH OPOR fear & fer oT 25cm B a
gute aft at $, Rate tix pate @ §] sak ate
hig
2 ew at were ara f, tar cater 7 by wt
suv © aor ra rhe
{ay 15
(by 17
(e)20
(a) 22
182. 0 is the center of bigger circle. 6 identical
circles of radius ‘r' are drawn. Radius of bigger
cirele is 10 cm.
Wm et Oo Br Ree 6 re Bw Ot
att] 98 qa A Psat 10cm B] r=?
(a) 10/3
(b) 10/6
{) 10/7
(a) 20/7
183. In fig. ABC is a right angled | with Bas
right angle. Three semicircles are drawn with
AB, BC & AC as diameters. What is area of
shaded portion if area of 4 is 6 square units.
arpit 4, aBc wn wore fas FB EI AB,
Be afte Ac 1 earer reT ator ante at at fy
arate ser a eb are AAS, aA Pagar sr
are 6 ot yrs Bi LP te OE ZS
MENSURAT ION
INSP. MOHIT GOYAL SIR
P Q
(0) 22.63
(&) 28.62
fe) 24.64
(4) 28.51
174, MNOP is a square of area 64 cm’, SM =
‘Jem and QO = 4em:, Find shaded area if RSQN
is rectangle.
MNOP ws a4 § faawr ea 64 em’, SM =
Jem, QO = 4em 61 Sraifra etre aie Hise
af RSQN UF arya BI
R s
a w
ta) 65/3
(b) 80/3
fe} 70/3
(4) 85/3
175. The diagram shows the net of right circular
cylinder. Find volume of cylinder.
fee 4 gare daa wr ae Raver aT eT
areata Pa
eo
176. Find ‘x’ so that volume of the U-shaped
rectangular structure is equal to 165 cm”.
re RTE, AE U SR AF ATATOR. aTBA
STRTT 165 cm? bi
10
(9) 7.5
(7
(4
(as
177. Pind the radius of biggest possible
semicircle that can be inscribed in a square of
side 2 cm.
afters agua f Prear ara fate at 2em spar
aa wh & seat ware aT BP
(a) 8-2/2
(b) 6-22
(ce) 4-23
(a) 10-22
178. Find volume of square pyramid formed by
given figure.
2 ag arp a, ote Reais er areca ae
fare
100/115,
3
200/115
3
100/119
6
«
()
te) MATHS FOUNDATION BATC
(a) 16cm:
83. An equilateral \ of area 300cm? is cut from its
three vertices to form a regular hexagon. Area
of hexagon is what % of area of triangle?
[eH TAME A 97 HTH 300m? B, Fat eit at
meet ww Praia wee TART Tar 81 CT TT
aerver, Raps etree ot Paar % BP
(a) 75%
{b) 50%
(c} 33.39%
(a) 66.66%
84. What is the total surface area of one side open
cubical box of outer side Sem & thickness
0.5em?
oF OF ame Re mT aeph qRoe Sane AT
thn, at ew ste kaa B, site wee A np apa
Sem ¢ sit HITS O.5cm bP
(a) 1.1m?
(b) 22cm?
fe) 33cm?
(@) 444em?
85. The volume of cuboid whose sides are in ratio
of 1:2:4 is same as that of cube, What is the
ratio of length of diagonal of cuboid to that of
cube?
Bw CARE See Uw wer A aT TATA BI
war Ft Te 1124 & asa BL ea Ow
Reet aang atte ot & Reet Fr wens
aera MT ePT?
(a) J7:5
(b) V7:6
fe) ¥7:2
(a) W733
86.4 corner of a cube of side length 8m when cut
by a plane which bisect the side of cube, we
get a pyramid whose volume is:
Ben TR EST ATA OO eT ST oe OF
de car aT AY at ET Te A eT aT B
at et on Profits Greer & fare arnt =?
(a) 8.37 (b) 11.20
(c) 10.67 (4) 9.68
87.In the given fig. ABCD is a square of side
idem. E & F are mid points of AB & DC resp.
Lad
MENSURATIONE sie
(atatata) INSP. MOHIT GOYAL SIR
EPF is a semicircle whose diameter is EF.
LMNO is a square. What is the area of shaded
region?
O ag ampfa 4 aBcD vw a4 § fraF aT 14cm
Be ait F sort; war AB ait Do % aeaRiey &
ae EPF Uw xQuqe § fare ce EF b LMNO
ew af $1 orate eer eT era aT TP
F
{ IN,
VW
€
(a) 92.5 em?
(b) 98.5 cm?
tc} 96.5 cm?
(4) 94.5 cm?
88.In the given figure, PQR is an equilateral 5
with side 120m, S & T are mid points of sides
PQ & PR respectively. Area of shaded region
>
Qa angi A, POR ww ara Fags 8, et
aT 12cm $1 8 aft T AEST PQ att PR & RUA
Bi wraifise ar eT dawer Far Be?
(a) 1003 (b) 12\3
fe) 14x83 (ay x3
89.A cube of side y is converted to a cuboid in
such a way that three concurrent edges are in
ratio 1:2:4 & shorter edge is x. What is the
ratio of surface area of cuboid to that of cube?
Aa y are wat BY eT Ht ga wT Aafia Ara
‘ara & Pe ati were Peart 1:24 & argra # ot
afte ter Rarer ac BH ToT PSS TET AT UT
4 arma & stare Pract bP
(a) 6:7
i)
(a) 7:6 MENSURATIONE rr
peey INSP. MOHIT GOYAL SIR
(e) 25+ 7.50
(a) 25-7.50
169. Acone of height 15cm & radius 6em is,
trimmed sufficiently to reduce it to a pyramid
whose base is an equilateral 4, then volume of
portion removed =?
ww tip Brat Sarg 15cm b att ftom 6em 8, 7
cow Rafts sere aa 8 Breer sree weraTg 3,
BY Bere are oer wT areca AT BIT
{a) 1802 -135¥3
(b) 185% - 1358/3
(c) 190% -135y3
(4) 1954-135/5
170. The square in the figure has sides with
length 9m. The radius of the circle is 2em.
What is area of shaded region?
amp a ah aor A eM Oem tH aT A
freer dem 81 fer a or ede war RT?
(a) 67-37
(0) 7-30
(c) 65-37
(a) 45-30
171. A3-meter square & a 4-meter square
overlap as shown in diagram. D is center of
‘3m square. Find area of shaded region DGFE?
ee 3h at ae Ow 4h wh Ow Gt nT ond F
ater apf 4 Rear aan 81D, 3 Me wh wT ae
0 oraifer ner DerE a ere ane HTT)
ani
(6/5
(b) 9/5
{e} 4/9
(a) 974
172, If BC pass through center of circle, then
area of shaded region =?
ait Be ae & tem & gor art F at waif ATT
am ene aT er?
B
173, Find area of shaded region, if PQRS is a
square of side 8 cm, RT = 2 cm and QU 1 PT.
ariifiea arr oT ewe wid fifaie, a PORS eH
= 8, faa aon Bem, RT = 2cm a QULPT
t DT askoieiihcseh hele ad
164, An equilateral triangle with side ‘a’ is
revolved about one of ita sides as axis. What is
volume of solid of revolution thus obtained?
ew aorng Fray fre aot tat §, ew ao
segee waren ara bi qart ae at ore apie wet,
SR APART FAT TAT.
a
165. ABCD is a square & AE = AF = CG = CH, AB
= 5 & the shaded region is five-ninths of area
of ABCD. Find AF =?
ABCD U¥ @ f aff AE = AF =CG=CH, AB=5
ait oraifve era, ABCD % chem 5/9 br
AP mT ae vet Afar)
A E
D 6
fa) 5/2
) 5/4
(5/3
(a)s/6
166, In the figure, point A is the center of a 100
x 100 cm square. Find 'x’ such that shaded
region has an area that is one-fifth of area of
square.
api 4, fig A, 100 x 100 om ww x hh
afte reife er er etree, wt A aT AT 1/5
6 ta 8am a Fifer
Ty
(a) 37
39
te} 41
ta) 43.
167. A square of side ‘a’ is inscribed in a circle
‘as shown. What is area of shaded region?
em ot fate ator ta! Few ge A ace WATT aT
1 Star Rewer aren 8, writ rer wT TAT aT
Aa
” (52}e
B42) 4
o (7)
vo (255? a"
14 & 202
168, ABCD is square of side Sem. At the four
corners, four circular arcs each of radius lem
are drawn. A circle of radius 2.5em with
centers drawn inside the square. What is area
of shaded region?
ABCD OF aff forrf HoT Sem t, UAT FT TT
Fe TOOT wo ware oe get A Fea lem
Bit 8 Se 2.Sem fom 8 Oe TT ET
& araife eer wr Gawe Far grr?
(a) 25484
(b) 25+ 7 ee
=,
ta) HT 6
159, Equilateral SABC has side length 1 &
squares ABDE, BCHI & CAFG lie outside the
triangle. What is area of hexagon DEPGHI?
‘wry ape ff aT ft wang 18 sit Tt ABDE,
BCHI ste CAPG Prager & ange Fea Bi SCAT
DEPGHI W we FUT BT?
(348
b) 443
fe) S43
ta) 100
160, The figure is made up of rectangle RSTU.
RWV is a straight line & VT - RX, SV/ST =?
avpit a ReTU ara t) RWW er eet tar faite
VT = RX, SV/ST =?
UT
MATHS FOUNDATION BATC
aMENSURATION
triangle. If triangle is placed on square, it can
cover up to 2/3 of square. Then area of 4 is:
‘AAG UF Gem x 6em a ww fe F or fer F,
at ae Pipa 91 60% APT Oy Har 81 aie Pes,
fe Sat var art at ay et eT 2/3 HPT eat B
finger vr ere = 2
(a) 44cm?
Six regular hexagons surround a regular
hexagon of side length 1 as shown. ar\ABC =?
1 weg an ar & Praha oR & ar 3 6
Prafta wey fea 6, ABC eT Brera =?
ta) 6V3
) 48
te) 3
ta) 3/3
163, In the given fig. two squares are placed
side by side. If area of larger square is 400 m?,
then area of shaded past is:
ag ampia A et wh were Ta a i ae as
FT QTE 400 m? &, at Brera OTT eT TTT
wm ore
A D
iG
5 CF
(=) 220m
| LP OS) |
ATION
BATCH
MENSURATION
(GEG)
att sonea dear * at & Ponsa aft ft mao
ww at aa Fife?
fa) 32
(4) 33
155. The figure shows square U & square V
inside square QRST. The area of square U is 49
cm’, Find perimeter of shaded part.
Rar 4, af use ah vow ot ORST & aT
eva 01 of OW etre 49 cm? §, erie ATT
am sftrt mea Fifer
5 R
T Q
fa) 55
() 44
fe) 66
(a)7
156, In the figure, area of square K is 36 cm" &
area of square Lia 225 cm, Find perimeter of
figure.
amp rf 97 eee 36 om? § at ot LT
awe 225 em? BL amy nr fore ara APE?
co
(a) 86
() 84
{e) 87
(ass
157. QRVW & STUV are squares. The area of
STUV is 100 cm?. Find the total shaded aren
in figure?
QRvw at sTuv at 1 STUV # ETT 100 cm?
1h ga orale eT area ae ATC
v 1
we“
(a) 144
(b) 148
(9) 146
(a) 150
158. A round table has radius 4, six rectangular
mats are placed on the table. Each mat has
width 1 & length ‘x’ as shown. They are
positioned so that each mat has two corners
on edge of the table, these two comers being
end points of same side of length x. Further
these mats are positioned so that each inner
comer touches an inner corner of an adjacent
mat. Then ==?
ee atareR Har A Rear 4 BB: aT ACTS
Ha OA aS Bi Tete wens ater 1 Ee
weang x 6, star Barn aa 8) 2 3a GK fra &
Se wed wcrg ch set Aa tet oe 1 oa dat
set fr after Reg, woe aT x RENE a ET
atte Poe a areas ger one Pere FO seat ae ht
ave 4 ert wad Bx =?
a) 7S
Dako dalbin ake eal MATHS FOUNDATION BATCH
MENSURATIONE ci
El INSP. MOHIT GOYAL SIR
Uw dearer aia farewT eaRT 24cm &, 4 ya Tt
1B) aR Gem few & aR ae oat A ara Rt oe
ar 8 phe: ge a an, at a tN
Freeh Seng aor sere
(a) Som
(0) 10 cm
{e) 16cm
(4) 12cm
150, A square pyramid of side 16 cm & height 6
em is cut at height 3 em from base by a
horizontal plane parallel to base & part left is
a square shaped hole of cross section area 1
cm’ is drilled across the body. Find the total
surface area of remaining body.
ew were Frais Fae HAT 16 em ate Su 6
om 6, SU FS cm H Sas Tt eta at
ere Ter are Fa a ST APT, eH HTT
¢ fawer aqyey wr ey Lem? 1 at we Ee
ar sor par geste ahem a ARTE]
(a) 560
) 380
{) 570
(a) 580
151. The length & breadth of a rectangle given
below are: 80 cm & 40 cm resp. If this
rectangle is divided in two equal rectangles, 2
‘equal squares & a shaded square, then area of
shaded equare is:
ew waa A azang atte cieg wae: 810cm ae
40cm 1 ait ay area a waet aad A, at war
wt ake ew wraifita wt A wer rab at
reife oh nr err aT ETT?
Alp
c
D
(a) 250
te) 400
fe) 200
(a) 500
152. Find volume of combined body.
yet amp wr areca wa Ae]
11802
3
11605
3
12602
(5
(a),
153. A cylinder of radius 7em height 14cm is
Placed over a hemisphere. If cylinder is cut by
two planes parallel to its base at height of 2
cm & 6 cm from top. & cut parts have volume
as shown. V1:V2:V3:V4 =?
ew tat fara feat 7em & att Sarg 14cm 8,
Wer Herat & Sa Tar Ol ae tar Hot aT
are amare & ania, eh & 2em site Gem 4
‘Sang oe wer oar B a Vi-v2ivaeva = 2
13607
3
(a) 3:6:12:7.
{b) 7:12:6:3,
fe} 3:7:12:6
(4) 6:12:7:3
154, ABCD is a square with AB = 13, points E &
F are exterior to ABCD such that BE=DF=5 &
AE=CF=12. If EF can be represented as min,
where m & n are positive integers & m is not
divisible by square of any prime no., then find
m xn?
ABcD Uy wi 8, Brat AB= 13, fig Bate F
ABCD gC Ra WHT Pua F Pe BE=DFHS att
AE-CF=12 8] 27% EF #1 myn @ wea Aen 7a
6 af m aR a Tee Pt dem Fate m Pet MATHS FOUNDATION BATC
ashe ie ai seh hel ead
-.) =
Y tt On
I 1115s
wt Ree fear var 8, fox ew wr maT Fe aT
fee Fear aT G] car Ow aT GT we Ate AT Pe
fen aan bl aS ea seer she wit wa F aa
2 aqua aT Bia
fe) 1:2/3
fb) 2V3 21
(e) 3V8 21
(a) 1:35
145, A 3x3x3 cm cube has three holes each of
In] cm cross section running from center of
each face to center af opposite face. Then
total surface area of solid so obtained is
WW 3x3x3 cm wa A dr Oe B, WAH Ix em
ERT re Wee ae Hea a oe aa
Sea a arate ach OT aE aT ga aT
ea oft
(48
) 24
(€)36
(a) 72
146. Consider a right circular cone of base
radius 4.0m & height 10 cm, A cylinder is to
be placed inside cone with one of flat surfaces
reating on the base of cone. Find the largest
possible total surface area of cylinder?
ew gored ig anu Azar 4 em} ate Sanh
10 cm bi UF tea tip & arex van 6 fart oF
way eR wT TE By da wT af FT TST
err aia Hae
tm) 2508
100%
3
®)
500%
oS
200"
jay 200"
a7
147. An oil funnel made of tin sheet consists of
2 10 cm long cylindrical portion attached to a
frustum of a cone as shown. If total height is
22cm, the diameter of cylinder is Bem &
diameter of top of funnel is 18cm. What is
area of tin sheet required to make the funnel?
er ae fT aot ft & wh 6 fae wens 10
com 8, aig & sre & daar aren ay ats ra
br ate qe Sang 22 om §, Aer Hoa 8 cm
att ae FT ART 18 om 6, ot ae FT TAT
few React fear 1 anaersar grit
44
(a) 2460
(b) 2487
te) 249%
(4) 247%
148. What is total surface area of largest cube
inside a hemisphere of radius Gem such that 4
vertices of cube lie on the base of
hemisphere?
wer aftr wr eT Fea PST area aT eT a
UF 6 cm Prem & ater & sex ge oer 6 Pe
Ga & 4 att adueta & ame we Rea Fe
(a) 155
(o) 144
{c) 166
(a) 154
149. A cylindrical vessel of diameter 24 em
contains some water. If four spheres of radii
6cm each are lowered into water until they are
completely immersed, then water level in
vessel rise by: MATHS
TION BATC
Te soi he toh oot ead
FOUNDA Lat
MENSURAT On
(
the amount of water is 25% of tank
capacity?
ee a eh ar tan ow set gee cig aT
ti se% sre #1 Roa 16 foe & atk Sah 96
Ree ti few A ort A Sarg ar GN ae set Fy
are Ow A evra $1 25% BP
(a) 4802
(b) 1672
fe) 3232
(a) 6492
125. Find the volume of regular tetrahedron
with side length lem.
vem Rafter eqenene at aaa anet ae rH
a1 1em 8?
TS)
@) To
fb)
fe)
Slim oli oli
ay
126. Find the distance from vertex B to face
ACD if ABCD is a regular tetrahedron with
side length 6.
aa aco #, ot Ba a are Paw, ze ABCD
ew rafter aqenere B Raa gat 6 81
fa) 25
(b) 2V7
(e) 2V6
(a) 28
127. Four of the eight vertices of a cube are
vertices of a regular tetrahedron. Find the
Tube
ratio of total surface area of cube to surface
area of tetrahedron.
Teme as a of ao a Oe Prat
sage A a 1 eer ite eqs ar ged
Sewer 1 aequa ae ARC
fa) ¥231
(2
fe a:
(ay V1
128. In the rectangular parallelepiped
ABCDEFGH below, AB = 4, BC = 3, CG = 9, BY
= 8 and DX = 5. Find the value of XY.
fe WTAE AHIAT TFT ABCDERGH H, AB = 4,
BC = 3,CG=9,BY=3 sit Dx=5 t1xY WAM
ana Pefore
A B
(a) 23
(b) 28
te) ¥26
(a 29
129. Ina cube ABCDEFGH, ABCD is a face & M
iz mid-point of edge DE, BM =?
1 WH ABCDEFGH #, ABCD Uw aw Bait M
Tar DE eT Aeahees $, BM = 7 130. What is volume of regular octahedron
whose vertices are the centers of the faces of
a cube whose edge has length 6?
ew Pratt soviet ser aractet rar ptr fara
a oe cr at oF tee bathe oA aT
wang 6 tr
fay 12
(0) 36
fe) 24
(a) 48
131. Find the volume of « regular octahedron
with side length lem.
op Prats sects er sract met Afar fet
agar tem te
(ap 1/v2 (b) 2/3
fe) 1/32 (a) 23/3
132. A cone of radius 3 cm & height 4 cm is
placed vertically inside a cylinder of radius R
such that it fits exactly inside the cylinder as
shown, then R=?
3 om four IN 4 om Sag HT UH Te UF tat F
eR We Tar ren &, det AM Hea R Bl R=?
fa) 25/4 (25/8
fe) 8/3 (a) 7/3
133. A pyramid has a square base with side of
length 1 & has lateral faces that are
equilateral As. A cube is placed within pyramid
80 that one face is on the base of pyramid &
opposite face has all its edges on lateral faces
of pyramid as shown. What is volume of this
cube?
ee Rafts er arene we at & forret aor fT
wag 1} ste aeyedre ae wry &] Rafts
Fe OW UF Fe TER Ta aan & A Ge OH eT
rafts & arene oy fea & atte Prete er ath
agar Prats @ wwyen oe fee f, Sar Rear mar
31 oee ea amet Fan CPT?
nT
(a) 5\2-7
{e) 92/9
(7-413
(a) 43/9
134, Two spheres of equal radius are taken out
by cutting from a solid cube of side (12 + 4\3)
om, What is the maximum volume of each
sphere?
ware fear ch att Ow ore oT THe a
‘Sreé ao (12 + 413) om Fl Tew A HT
afew Hat FAT BPP
(0) 2887
(144,
(c) 432"
(a) 664
135, In the adjoining figure of rectangular solid,
2DHG = 45° & 2FHB = 60°. Cosine of
(@
slo
123. Find area of \BDE, where ABCDEFGH is «
cube, AB = 6
ABDE #1 ehawat ait Fifer, wet ABCDEFGH TF
ua t, AB=6
fa) 173
{b) 15/5
te) 18/5
14) 19/3
124. The water tank in the diagram is in shape
of an inverted right circular cone. The radius
Of its base is 16 feet & its height is 96 feet.
What is height in feet of the water in tank if MATHS FOUNDATIO'
10cm. Total surface area of prism =?
ee Broa ar are we aaeioT Papa ¢ fore
prt Som at 12cm Fi Rew AY Saf 10cm t1
east wr ye Glow ehren =?
(a) 300
{e) 360
(b) 330
(a) 325
111, Ialtitude of right prism is 10cm & its base
is an equilateral 4 of side 12cm, then total
surface area =?
af ww Bren Ft Sang 10cm 8 att FHT TTT
ew worang Pea & faa AST 120m ¥, a yO
eave =?
(a) 75 548
(b) 25 54/8
fe) 50 5+ 3
(a) 150 543
112. The right pyramid of 6m height has a
‘square base of which diagonal is \1152 m,
volume =?
em frais 7 Sa Gem $ athe ane oT aH
Fart Preot 1152 m %, waa =?
(a) 144 {o) 288
(€) 576 (a) 1152
113, The base of a right prism is an equilateral
\ of area 173 em? & volume is 10380 em,
Area of lateral surface of prism =?
oe Rrra aT ee wg 4 8, ree eT
173 cm? § 3K ST 10380 cm? F| Rr
rea Fa sre
(a) 1200 (b) 2400
fe) 3600 {a) 4380
114, There is a pyramid on a base which is
regular hexagon having side 2a, If every slant
edge of a pyramid is of length 5a/2, then
volume of this pyramid =?
vow Pres: ar are wae rar Nearer Fre
Rat 2a bi aie Rufts $1 sete few Say 50/2
1B at Serer are FT BPP
(ap 308 (a) 302/V2
te) 302/13 (4) 6a
115, All five faces of a regular pyramid with
square base are found to be of same area. The
height of pyramid is 3 cm, total area of all of
its surfaces is:
ue Prafta Profs fore sma ww at &, © wat
fe arm eoewe ww wae bi Profs Mt Sef 3
om 6, at sent watt weet wT per Tete awe
wm:
(8 (b) 10
(12 (a) 16
116, Area of square base of right pyramid is 64
cm*. If area of each triangle forming slant
surface is 20 em? then volume of pyramid =?
er wthne sTUR Peres HT ewe 64 cm? 6, we
feats eae ET Tote Fp aT eer 20 em?
%, at Rafts 1 sears?
(a) 32
(84
(e) 74
(a) 64
117. The base of a right prism is an equilateral
A. If Interal surface area & volume is 120 em?
& 4013 cm® resp, The side of base is:
ve roo or are arg. bi ait ww yor
Seve she ara Bae: 120 cm? SK 40)3 cm? f,
at ana Ff aan = 2
(a4 m5
(7 (a)40
118. Find volume of a right priam which is
based on regular hexagon of height 10 cm, if
it's total surface area = 156V3 em??
co ease mr aerator fae FT aT aT
Bott Saf 10cm & sit gem Fa ToT
SFT = 156\3 cm? F)
(a) 3643 MATHS FOUNDATION BATC
H
MENSURATIONE Zc es
eee
poh 6S + TT
fe) 53 + aT
(a) 6Y3 +7
103. In a parallelogram ABCD, AB = 24cm, AO =
BO = 13cm, then BC =?
UF ABCD Wat Wate Ht AB = 24cm, AO = BO
= 13cm, BC=?
(a) 10 cm
b) llcm
fe) 120m,
(d) 14 om
104, A pyramid fits exactly inside a box. What is,
ratio of volume of pyramid to volume of box?
ow Prats ew wey sex Tar arb) Profs:
tke weet as rare ny arep aT GPT
(a) 18
b) 1:4
fey 5
(a) 3:1
105, The base of a right pyramid is
equilateral triangle of side 4 cm. The height of
pyramid is half of its slant height, volume =?
er Prats a sree ew ary Pla ber
Ha dem bi Paits # San get ten Ferg A
ant t, area =?
106. A right pyramid stands on a base 16 cm
square & its height ia 15 cm; area of its slant
surface is:
Ow TARTS ITU 16 cm? t, aie Fee Sony
1Sem 6, sa Row sae HT Te =?
(a) 514 (b) 544
to) 344 (ay 444
107, ABC company packed a product for
shipping by wrapping tape around package as
shown. An additional 10% length of tape
package is needed for overlap. What is total
Tength of tape needed per package?
Ase Sh we arnt te ect 8, ferent re
ant aw ty warren ara & star fe cette ara by
Weaw tee & fw 10% afte wears A te
arena ore 8) fa tine Reet oo Fy arTePPAT
whe
15
(a) 140
{b) 255,
(e) 210
(a) 110
108. From a circular sheet of radius 25cm, a
sector of area 4% is removed from the center.
I remaining sheet is used to make a conical
surface. Then what is the ratio of radius &
height of cone?
25 cm Rem % UW ARE FIs FT 4% CTT
ew aio Aiea ater rar aan Bi a we rT
the ow cig are ae eh ac at Peat
ate San TE a Sere
(a) 24:7
(b) 7:24
{e) 12:7
(4) 7212
109. On the top of a cubical box, a pyramid is
placed; base of pyramid being equal to top of
box, height of pyramid is twice the length of
box. Ratio of volume of combined body to that
of box =?
er Car See & TF Soe, ww Paes bl
Profs sr smug wrt & seh ar h Tae B,
Rrafes ft Seg wet fr res oH cept at gt
MAR Ta a A ere HT STAT aT CTT?
(a) 23
(b) 3:5
(e) 5:3
(a) 3:2 MATHS FOUNDATION BATC
& 4 Lal
ees
fe) 543, \aeee Pp
77.ABCDEF is a regular hexagon of side 12cm, 4 a
What is area of ABCD?
ABCDEF 6 Fraftta sca & fete aT 12cm
Bi aecp #1 eawa FaT BPI? T R
(a) 183 (b) 243
(e) 36v3, (a) 42v3 s
(a) 162\3 (0) 216v3
78.10 « parallelogram, base = 10, height = 5 and {e} 1083 (a) 54v3
longer diagonal = 13, Shorter diagonal =?
ew wae Sepia H aTUTE = 10, Sf =5, AFA «81. ABCDEF is a regular hexagon. Ratio of area of
fret = 13, wher Pet = > shaded region & area of unshaded region =?
pen ABCDEF ww Praia seas & a aire a eT
1 Aer sree ror ebro wT STITT WPT?
(o) a7 B
(a) J89
79.1n the given figure PQR is « triangle &
quadrilateral ABCD is inscribed in it. QD =
2em, QC = Sem, CR = 3cm, BR = 4em, PB =
Gem, PA = Sem & AD = Sem. Area of
quadrilateral ABCD =?
2 ag apis 4, POR ww Pape fate gah ace
ABCD ® Wats Fira zat Fl QD = 2em Qe =
Sem, CR = 3cm, BR = 4cm. FB = 6cm. PA=
Sem 3K AD = Sem, TYAS ABCD #1 RaW =? tas
82.In the given figure, ABCD & BEFG are squares
of sides Scm & 6cm resp. Find the area of the
shaded region =?
21g apf # aucD atk BEFG at F Pert
agand sort: Sem af Gem EI write ar FT
aww =?
D e
F c
ta) (23V21)/4 {by (15V21)/4 eH
fey (17V23)/5 fa) (2321)/5. }
6c
80. In the given fig. PORSTU is a regular hexagon
of side 12cm. Find the ar. ASQU =? x E B
a ag sinpftt 4, PoRSTU Uw Prefer soa 6 (0) 12 cm?
fae HAT 12cm F, ASQU RT eorwe =? (b) 2¢em?
{c) 18cm?
wT @ bn OA OOF OS
Te askoieihcneh eel ead
Lad
A ee On
‘90. The total surfact AGES
rectangle whose diagonal is equal to 4m
forms an angle n/6 with base. Volume of
cylinder =?
ew dere FT YO ew srr a oor E Aaa
feet an Boa we 8/6 FT WaT BI
‘eee Sarat aT CrP
fa) 6x
) 8x7
(e) 1ax*
(ay 1827
91. right triangular pyramid XYZB is cut from
cube as shown in figure. The side of cube is
16cm, X, ¥ & Z are mid points of edges of
cube. What is total surface area of pyramid?
or Peper Rats xyze www oT Swe TT
Baten ap A ater arab) wa A AST 16cm b,
x, ¥ aie Zot A malt & aeafieg $1 Ras a
FH pdt arava a Siar?
(a) 48 341
(b) 24 541
fe) 28 6+ 3
(a) 32 3+ V3
92. Right pyramids are removed from each corner
of a cube of side Sem. Four of them are as
shown. T.S.A of body =?
Bem Rat ow uae ae Prats, us a wie
wnt & aren fir ore G1 sat & a Rare art 6,
gt anger a par pede etamar aT era?
(a) 42443
() 4814/5
e) 42+ 8V3
{d) 4246/3
93.1n a cube of side Sem, eight pyramids are
removed from each comer of cube. Four of
them are shown. Then,
volume of 8 pyramid /Volume of remaining
solid?
Sem Aart & ew ua 4, uetw eh a 8 Ras
aor Fist ara G8 Prats wr arma / wet oer
at =P
(a) 3/77
(b) 2/77
te)4/77
ta) 6/77
94.A cube of side 4 cm is cut by 3 planes into
four parts. Its 1st & 3rd plane bisect the side,
then ratio of volume of four parts V1: V2: V3:
va=?
4 om aT 8 ew war YO aa ORT a HT
were a | Teen ate AT Ar apa eT cy ait at
saree & at at aot #6 rear THAT VI: V2:
va: v4 ea BIT?
(a) 1:3:3:1
(b) 3:3:1:1
95.A cylinder of radius 7em & height 14cm is cut
horizontally & vertically at h/2 as shown & a
part is removed. Total surface area of
remaining body =?
Pet 7em at STS ldo wwe Reise Meret
athe sweet Bo H b/2 TC IT oe F aT Pe
‘aren war & atte ow feea per Rar ara bi ee
ainpier er per pede ere Fa eT?
(a) 779
(b) 889
tc} 886
(a) 888
96.in the given figure, find the ratio of volume of
‘a small slice to a bigger slice?
87g ampfa Aart oe ate wy oes area aT
SUN a eT? &
(a) 3/4
(o) 3/5
(c) 3/7
(a) 3/8
97. String when wound on exterior four walls of a
cube of side ‘n’ cm starting at C & ending at
point D can give exactly one tum. Length of
string =?
Se com aT a ar A RS Tea
ait arch tat ct a ots Bathe De are eit
8 at FR ee wee lt 8] ee A et eT
arte
(a) Ji9n
(b) in
(c) V2?
(a) Ji2n
98.ABCD is a parallelogram. AB = 10cm, AD =
6cm and angle bisector of 4A meets DC at E &
meet BC produced to F, then CF =?
ABCD UF Haat TPs t] AB = 10cm, AD =
Gem, 2A #1 TARRTAE DC HEV wea F IT
Be wt aged F oe Brea fat CR=?
(a) dem
(b) Gem.
(¢) Sem
(4) 10cm
99.6 slices are cut off from a cylinder at height of
h/2 as shown then ratio of volume of each
slice to volume of remaining solid =?
ww dar T h/2 Seg 6 CWS we ATE aT
Sete wh eT we Ge ake A aa OT RTT
a ePTT
(a) 1/7
(b) 1/21
(e) 1/42
(a) 1/14
100. Area of circle varies as square of its radius.
I area of circle of radius 10 cm is 300 em?,
‘then what is area of circle with radius 12 cm?
rr Sree set Row wt v4 t] we 10cm
ear & yw ere 300 cm? § at 12 cm THT
ee eee ar eT
(a) 422cm?
(b) 322m”
(e) 120m?
(a) 42cm?
101. In an equilateral AABC, AO, BO & CO are
angle bisectors, meet at incentre O, D, E & F
are mid-points of AO, BO, CO resp. A circle is
drawn with center 'O' passes through D, E & F.
Area of circle is 3nem?, perimeter of SABC =?
Ww AAaE SABC H, AO, BO aI CO wer
wacterar® & AM AO, BO, CO * ATG O, D,
Ear ot fret 1 I 1 Swe Sncm? t at
AABC "1 GPCATY =?
(2) 17 em
(b) 16 cm
(c) 18 cm
(4) 17 cm
102. The longer side of parallelogram is 10 cm
orter side 6 em. If longer diagonal makes
an angle of 30° with longer side, Length of
longer diagonal =?
waiet sepa A wan aan ate wet maT 10cm bi
aie aan Beech, weal ear & arr 30° er stor
warat §, at att Rewet A ang en ortte
(a) 6/3 + 13 MATHS FOUNDATION BATCH
a easkole hi eh het ead
MENSURATION
(c) 17,200
(a) 18,500
36. The height of cone is 30cm. A small cone is
cut off at the top by a plane parallel to its
base. If ita volume is of 1/27 of cone V, then
at what height above the base is section
made?
ww ig Ft Se 30cm bi Fa STU Tria OH
Ble eR ver are G1 AR gare seer hy VT
1/27 8, at aan & Pract Sears oe Bowie Ta 87
(a) 20 em
(b) 25 cm
(¢) 28 cm
(a) 22 em
37.1n the given figure, find the area of
quadrilateral ACDE?
fee ae fag a, api ACDE HT ara WT
Aiae?
c A B
Wa
-
D F
(0) 3.6em?
(b) 3.3cm?
(¢) 35cm?
(4) 5.5m?
8. The base radius slant height of conical
vessel is 3cm & 6em resp. Find the volume of
water that must be required when a sphere of
radius lem is placed into it and water just
immersed it?
ee STAR aeet FY are Prem ae Pere Seg
Sem 3 6em FI AE lem Pew we UH Tat Fat
an ave at pier part gw art at ott ret
en Fr arererrat eet?
10%
oS
39.A large solid sphere of diameter 15m is melted
& recasted into several small spheres of Sm
diameter, what is the % increase in surface
area of smaller spheres over that of large
sphere?
15m CURT TUR ST ote ata PRTAAT Im CATT
fe 5g Oe a ware re F, at ONE otal & BEE
pester Rena Hb ad Art 96 A at Be
(a) 200%
{(b) 400%
{e} 300%
(a) 250%
40.4 hollow right circular cylinder of radius r &
height 4r is standing vertically on a plane. Ifa
solid right circular cone of radius 2r & height
Gr is placed with its vertex down in cylinder.
Volume of portion of cone outside cylinder is:
em Gre Taran dat eh Prem e wer Sas 4r
6, ee waa He waa TaN Bi ae eH She EAT
aig Bratt fom 2c ae Seng Gr 8, Ft Aaa A car
sorte ah dar ange aig er er area aT
ern
(a) 9xr*
(b) are*
le) 7xr?
(a) 6xr?
41. What is the number of double cones of semi
vertex angle a having 'r' as radius of mid-
section which can be molded out of cylinder of
base radius 'r' & height 2r cota?
a Root chet ig ote Rea a tor @ 8, ae
Pisa tet &, sie er an eT age UW Meet wT
ar 8, fateh fear ‘er ae Saif 2r cota br
fa)
Hs
(5
ta6
42.A conical flask of base radius r & height h is
full of milk. The milk is now poured into a MATHS FOUNDATION BATC
Lad
eee ONE CONTEN
t INSP. MOHIT GOYAL SIR
cylindrical flask of radius 2r. What is J
which milk will rise in flask?
er iy are ds Pre aren Pea r Ter
Sangh Bg a ara But ae ew dao
acer Fave fear aren § fare Prem ar Bi act
Ge 8 aR Pree Seg aw soe
fa) b/5
(b) b/8
fe) h/6
(ay n/12
43. The radius & height of a right solid circular
cone (ABC) are resp. 6 & 2\7em. A coaxial
cone DEF of radius 3em & height v7em is cut
out. What is the whole surface area of
remaining solid?
ow ofr ey ape A fis ate Sef woe: 6 ate
2v7em Fi we wate tie Der ferrét rea
Seam ate Saf vem bse aren Bk ge aT
Fa geste erewe T ET
(a) 86n
() 89r
(o) 84m,
(a) 872
44.An equilateral triangle with side ‘a’ is revolved
about one of its sides as axis. What is volume
of solid thus obtained after revolution?
ee wag fags Gar yor a’ be eA or
agar & seein err aren By Gary ae ay ater
ampfa ah 8 seer areca Far ep?
ra®
ae
4
)
6
ae
45. If there is water in 1/3 of surface area of cube
then what portion of volume is merged into
water?
a ew wa A May Te 1/3 Te Bat ore HT
rear mer are a gar GST bP
(a) 1/6
(b) 1/5
tes
(a8
46. The radius & height of a right solid circular
cone is r & h resp. A conical cavity of radius
1/2 & height h/2 is cut out of cone. What is
the whole surface area of rest of the portion, if
both are coaxial.
wm oe Gare thy A Fear ote Seg were x site
b OG ew e/2 Rom ae h/2 Sap vy wee
rer were aire 61 Se ay TT Be TT
rer etree var ater aE chat her Fe
Smrve" +b? + Sux”
(gh
yy Orde +h + Snr?
4
le +h? +n?
ta) SR Po ome
47.From a wooden cylindrical block whose
diameter is equal to its height, a sphere of
maximum possible volume is carved out. What
is the ratio of volume of utilized wood to that
of wasted wood?
er aah & dearer vale &, fren cara seer
Sarg & wat ber ater rer are bh var FY ag
wed aor ent Rag aed aaa sep
0 orn
f)
fe} 4:1,
ta) 6:1
48.A right circular solid cone of maximum.
possible volume is cut off from a solid cylinder
of volume V. Remaining part is melt & recast
into four identical spheres. What is the
volume of each sphere?
V Sara ra ew he hee a OH HTT Ber
after aera HT eR Ter TAT Bl TT PTT
Rrearee are ear are AR Te, Tew tT
area aT BPP
favs MATHS FOUNDATION BATC
Lal
at ON
eee ees
TT-A solid metal phe Cuetec
to form small cones of radius 1.75em & height
3.5cm. How many small cones will be obtained
from sphere?
ew ake mg & ata HM fea 19em Fb, FAaT
Rrraret 1.75em Fea attr 3.5em Seg © wt
sig werd oF) Ph OnE dy aN ST oT
ara Fe
(a) 512
(c) 1026
(b) 256
(a) 2048
72. The radius of base of solid cone is Sem & its
height is 21cm. It is cut into 3 parts by two
cuts which are parallel to base. The cuts are at
height of 7em & 14cm from base resp. What is
the ratio of curved surface areas of top, middle
& bottom parts resp.?
ww ake tig # Faw Sem f att Sef 2iem F
‘We MUR F HAT Ct He, BM Tom HT 14cm Ft
Sag 1 wae wa F, FaH Gar 9 at A wre
ara 81 a8, ger aren Pret APT ® qhow eT
73.im the given figure, PQRS is quadrilateral. If
QR = 18cm & PS = Sem, then area of
quadrilateral PQRS=?
a ag argia 4 PORS, UF apis Bi we QR =
18em 3K PS = 9em, at aPfsT PQRS W TWA =
(a) 64,3/3
(e) 1353/2
(b) 17¥3/2
(a) 98y3/3
74. In the given figure, a circle touches the sides
of quadrilateral PQRS. The radius of circle
Tube
‘Sem, CRSP =