Mensuration - 3D
Mensuration - 3D
A
3. A hollow cube is made of paper to have a volume SS
of 512 cubic units. How much paper in square (a) 10557 cm³ (b) 10560 cm³
units will be required to make the cube? (c) 10555 cm³ (d) 10551 cm³
,d •ks•yk ?ku dkxt ls cuk gS ftldk vk;ru 512 ?ku 9. The sum of the length, breadth and depth of a
bdkbZ gSA ?ku cukus ds fy, oxZ bdkb;ksa esa fdrus dkxt dh
Y
cuboid is 23 cm, and its diagonal is 5 7 cm . Its
vko';drk gksxh\ surface area is:
SSC CHSL TIER-II 10/01/2024
,d ?kukHk dh yackbZ] pkSM+kbZ vkSj xgjkbZ
23 lsehdk
gS];ksx
(a) 384 (b) 328
vkSj bldk fod.kZ5 7 lseh gSA bldk i`"Bh; {ks=kiQy D;k
4.
(c) 348 (d) 288
H
Three cubes with sides in the ratio of 3:4:5 are
melted to form a single cube whose diagonal is
gS\
SS
18 3 cm. The sides of the three cubes are: (a) 288 cm² (b) 354 cm²
(c) 372 cm² (d) 222 cm²
3 : 4 : 5 d s vuqikr esa Hkqtkvksa okys rhu ?kuksa dks fi?kykdj ,d ,slk
S
10. A room is in the shape of a cuboid, with dimensions
?ku cuk;k tkrk gS ftldk fod.kZ18 3 lseh gSA rhuksa ?kuksa dh Hkqtk, 12m × 10m × 3m. What is the cost of painting the
____ gSaA four walls of the room at the rate of `50 per sq.m?
SS ,d dejk ?kukHk ds vkdkj esa gS ftldh yackbZ] pkSM+kbZ vkSj
K
5. A solid cube, whose each edge is of length 48 cm, (c) `6600 (d) `7500
is melted. Identical solid cubes, each of volume 64 11. The volume of rectangular block is 12288 m³. Its
cm3, are made out of this molten cube, without any dimension are in the ratio of 4 : 3 : 2. If the entire
wastage. How many such small cubes are surface is polished at the rate 2 paise per m², then
obtained? find the total cost of polishing.
,d Bksl ?ku] ftlds çR;sd dksj dh yackbZ 48 lseh gS] dks ,d vk;rkd kj •aM dk vk;ru 12288 ehVj3 gSA blds vk;ke
fi?kyk;k tkrk gSA bl fi?kys gq, ?ku ls fcuk fdlh viO;; ds 4% 3% 2 ds vuqikr esa gSA ;fn laiw.kZ i`"B dks22d iSls@ehV
h
,d leku Bksl ?ku] ftuesa ls çR;sd dk vk;ru 64 lseh3
gS] nj ls ikWfy'k fd;k tk,] rks ikWfy'k djus dh dqy ykxr Kkr
cuk, tkrs gSaA ,sls fdrus NksVs ?ku çkIr gksaxs\ dhft,A
SS CHSL 11/07/2024 (Shift-04)
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(a) 329431 cm3 (b) 217404 cm3 (a) 2508 cm² (b) 2260 cm²
(c) 819832 cm 3
(d) 192392 cm3 (c) 2550 cm² (d) 1580 cm²
13. The measurement of a right rectangular box is of 19. The respective ratio between numerical values of the
length 1.6m, width 90 cm, height 60 cm. Soap curved surface area and the volume of a right
cakes of dimensions 6 cm × 5 cm × 40 mm are to circular cylinder is 2 : 3. If the respective ratio
be packed in boxes in such a way that there is no between the radius and the height of the cylinder
empty space left in the box. How many cakes can is 3 : 7, what is the total surface area of the cylinder?
be packed in a box? ,d yac o`Ùkh; csyu ds oØ i`"Bh; {ks=kiQy vkSj vk;ru ds
,d yac vk;rkdkj fMCcs dh eki] yackbZ
1.6 ehVj] pkSM+kbZ
90 la[;kRed ekuksa ds chp dk vuqikr Øe'k% A ;fn
2 : 3 gS
lseh]ÅapkbZ 6 lseh × 5 lseh × 40 fe-eh- vk;keksa
60 lseh gSA csyu dh f=kT;k vkSj Å¡pkbZ ds chp dk vuqikr Øe'k%
3:7
okys lkcqu ds dsdksa dks fMCcs esa bl çdkj iSd fd;k tkuk fd gS
] rks csyu dk dqy i`"Bh; {ks=kiQy D;k gS\
fMCcs esa dksbZ •kyh txg u cpsA fMCcs esa fdrus dsd iSd fd, S
tk ldrs gSa\ (a) 62cm2 (b) 60cm2
S (c) 45cm2 (d) 65cm2
(a) 6500 (b) 5600 20. Two rectangular sheets of paper, each 60 cm × 36
(c) 6000 (d) 7200 cm, are made into two right circular cylinders, one
by rolling the paper along its length and the other
14. If the volume of one brick is 0.0014 m³, then how
along the breadth. The ratio of the volumes of the
many bricks will be required to construct a wall two cylinders, thus formed, is:
A
of length 14 m, breadth 0.125 m and height 5 m?
dkxt ds nks vk;rkdkj 'khVksa ls] ftuesa ls çR;sd
60 lseh×
; fn ,d bZaV dk vk;ru 0.0014 ehVj³ gS] rks
14 ehVj yackbZ]
36 lseh ds gSa] ls ,d 'khV dks mldh yackbZ ds vuqfn'k
0.125 ehVj pkSM+kbZ 5 ehVj
vkSj ÅapkbZ dh nhokj cukus ds fy, vkSj nwljs 'khV dks mldh pkSM+kbZ ds vuqfn'k eksM+dj
fdruh bZaVksa dh vko';drk gksxh\ o`Ùkh; csyu cuk, tkrs gSaA bl çdkj cus nksuksa csyuksa
Y
S
vk;ru dk vuqikr Kkr djsaA
(a) 5250 (b) 3250
S
(c) 6250 (d) 4250 (a) 5 : 6 (b) 8 : 3
15. Four cubes each of volume 216 cubic cm are (c) 7 : 4 (d) 5 : 3
area of the new solid is:
H
joined end to end to form a new solid. The surface
21. A patient in a hospital is given tea daily in a
cylindrical cup of diameter 7 cm. If the cup is
i zR;sd 216 ?ku lseh vk;ru okys pkj ?kuksa dks ,d nwljs ls tksM+djfilled with tea to a height of 4 cm, how much tea
,d u;k Bksl cuk;k x;k gSA u, Bksl dk i`"Bh; {ks=kiQy gS% the hospital has to prepare daily to serve 180
patients? [Use = 22/7]
S
S
(a) 1296 sq cm (b) 648 sq cm fdlh vLirky esa ,d jksxh dks çfrfnu 7 lseh O;kl okys
(c) 672 sq cm (d) 324 sq cm ,d csyukdkj di esa pk; nh tkrh gSA ;fn di dks pk; ls
16. Ranu carries water to school in a cylindrical flask 4 lseh dh špkbZ rd Hkjk tkrk gS] rks 180 jksfx;ksa dks pk
nsus ds fy, vLirky dks çfrfnu fdruh pk; rS;kj djuh
K
og cksry esa ys tk ldrh gSA 22. A drainage tile is a cylindrical shell 42 cm long. The
inside and outside diameters are 8 cm and 14 cm,
( = 22/7 dk iz;ksx dhft,) respectively. What is the volume ( (in cm³) of clay
S required for the tile? [Use = 22/7]
3
(a) 2372 cm (b) 2370 cm3
3
,d ty fudklh Vkby 42 lseh yack ,d csyukdkj •ksy gSA
(c) 2376 cm (d) 2374 cm3 vkarfjd vkSj cká O;kl Øe'k% 8 lseh vkSj 14 lseh gSA Vkby
17. A cylinder has a radius of 7 cm and the area of its
ds fy, vko';d feêðh dk vk;ru (lseh 3 esa) fdruk gS\
curved surface is 396 cm2. The volume of the
cylinder is: S
(a) 5241 (b) 4356
,d csyu dh f=kT;k 7 lseh gS vkSj bldk oØ i`"Bh; {ks=kiQy
(c) 4881 (d) 4125
396 lseh2 gSA csyu dk vk;ru D;k gksxk\
23. The curved surface area of a cone is 308 cm2, and its
S
3 3
slant height is 28 cm. Find the radius of its base.
(a) 1396 cm (b) 1381 cm
[Use = 22/7]
(c) 1386 cm3 (d) 1391 cm3
18. A cylinder of radius 7 cm has a curved surface area of ,d 'kaoqQ dk oØ&i`"Bh; {ks=kiQy308 lseh2 gS vkSj bldh
2200 cm². Find its total surface area. [Use = 22/7] fr;Zd Å¡pkbZ A blds vkèkkj dh f=kT;k Kkr dhft,A
28 lseh gS
7 lseh f=kT;k okys csyu dk oØ&i`"Bh; {ks=kiQy 2200 lseh
2 ( = 22/7 dk iz;ksx djsa
)
A bldk laiw.kZ i`"Bh; {ks=kiQy Kkr dhft,A
gS S
(= 22/7 dk iz;ksx djsa
) (a) 2.8 cm (b) 3.5 cm
S (c) 2.5 cm (d) 3.0 cm
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24. A solid cone with curved surface area twice its base 29. The radii of the ends of a frustum of a solid right-
area has slant height of 6 3 cm. Its height is: circular cone 45 cm high are 28 cm and 7 cm.
If this frustum is melted and reconstructed into
, d Bksl 'kaoqQ] ftldk oØ i`"Bh; {ks=kiQy mlds vkèkkj {ks=kiQy
a solid right circular cylinder whose radius of base
ls nksxquk gS] fr;Zd špkbZ and height are in the ratio 3: 5, find the curved
6 3 lsehgSA bldh špkbZ Kkr djsaA
surface area (in cm²) of this cylinder.
S
22
(a) 6 2 cm (b) 9 cm Use
7
(c) 6 cm (d) 3 6 cm
45 lseh Åaps ,d Bksl yac&o`Ùkh; 'kadq ds fNUud ds fljk
25. The volume of a cone with height equal to radius,
and slant height 5 cm is :
dh f=kT;k,a 28 lseh vkSj 7 lseh gSaA ;fn bl fNUud dks
fi?kykdj ,d Bksl yac o`Ùkh; csyu cuk;k tkrk gS] ftlds
f=kT;k ds cjkcj m¡QpkbZ5 vkSj
lseh fr;Zd maQpkbZ okys 'kaoqQ
dk vk;ru Kkr djsaA vk/kj dh f=kT;k vkSj ÅapkbZ dk vuqikr 3% 5 gS rks bl
22
S csyu dk oØ i`"Bh; {ks=kiQy (lseh
2
e sa) Kkr djsaA
¹
7
125 125 dk ç;ksx djsaAº
(a) cm3 (b) cm3
12 3 6 3 S
A
(a) 4610 (b) 4620
125 125
(c) cm3 (d) cm3
12 2 6 2 (c) 4640 (d) 4680
26. What is the total surface area of a cone whose 30. The radius of the base and height of a cone are 5
cm and 6 cm, respectively, whereas the radius of
r
Y
radius is and slant height is 4l ? the base and height of a cylinder are 2.5 cm and 3
4 cm, respectively. The ratio of the volume of the
cone to that of the cylinder is:
r
,d 'kadq dk dqy i`"Bh; {ks=kiQy fdruk gS] ftldh f=kT;k [Use = 22/7]
4
,d 'kadq ds vk/kj dh f=kT;k vkSj ÅapkbZ Øe'k%
5 lsehvkSj
gS vkSj fr;Zd ÅapkbZ
4l gS\
S
H 6 lsehgS] tcfd ,d csyu ds vk/kj dh f=kT;k vkSj ÅapkbZ
Øe'k%2.5 lsehvkSj3 lsehgSA 'kadq ds vk;ru vkSj csyu ds
r
(a) 8r(l + r) (b) r l vk;ru dk vuqikr Kkr djsaA
16
S
( = 22/7 dk iz;ksx djsa
)
r SSC CPO 28/06/2024 (Shift-01)
(c) r l (d) 4r(l + r) (a) 8 : 5 (b) 9 : 4
4
(c) 8 : 3 (d) 3 : 5
27. The ratio of the slant height and the height of a
K
cone is 4: 3. If the curved surface area of the cone 31. If the radius of a sphere is 2.1 cm, then the volume
of sphere is equal to:
is 4 7 square units, then the radius of the cone
;fn ,d xksys dh f=kT;k 2-1 lseh gS] rks xksys dk vk;ru Kkr
is ___ units.
djsaA
,d 'kaoqQ dh fr;Zd špkbZ vkSj špkbZ dk vuqikr 4%3 gSA
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34. Rajesh is playing with a football having diameter ,d v/Zxksykdkj ydM+h ds dVksjs dh Hkhrjh vkSj ckgjh f=kT;
of 28 cm. He wants to get a photo of his favourite Øe'k% 6 lseh vkSj 8 lseh gSaA bldh iwjh lrg dks ikWfy'k
player painted on the entire ball. The painter
charges `2/cm². What will be the cost (in `) of fd;k tkuk gS vkSj lseh2 dks ikWfy'k djus dh ykxr 50
painting the ball [Take = 22/7] ? :i;s gSA dVksjs dks ikWfy'k djus esa fdruk •pZ vk,xk\
SSC CHSL 08/07/2024 (Shift-4)
jkts'k ,d iqQVckWy ls [ksy jgk gS ftldk O;kl 28 lseh gSA
`12,000
og bl iwjh ckWy ij vius ilanhnk f[kykM+h dh rLohj isaV (a)
djkuk pkgrk gSA isaVj 2 #i;s@lseh
² dk 'kqYd ysrk gSA ckWy (b) `10,000
( = 22/7 dk
dks isaV djus dh ykxr (#i;s esa) D;k gksxh\ (c) `11,600
iz;ksx djsa
) (d) `11,400
SSC CHSL 05/07/2024 (Shift-01) 40. A sphere and a cube have equal surface areas. The
(a) 4,928 (b) 4,828 ratio of the volume of the sphere to that of the cube
is:
(c) 2,414 (d) 2,464
,d xksys vkSj ,d ?ku ds i`"Bh; {ks=kiQy leku gSaA xksys
35. Find the total surface area of a hemisphere with a
radius of 11 cm? vk;ru vkSj ?ku ds vk;ru dk vuqikr Kkr djsaaA
SSC Phase-XII 25/06/2024 (Shift-04)
11 lseh f=kT;k okys vèkZxksys dk dqy i`"Bh; {ks=kiQy Kkr djsaA
(a) 3: (b) 2:
SSC CPO 27/06/2024 (Shift-02)
A
(a) 242 cm 2
(b) 313 cm 2 (c) : 8 (d)6:
(c) 273 cm 2
(d) 363 cm 2 41. A hollow sphere of external and internal diameters
of 10 cm and 6 cm, respectively, is melted and
36. The diameter of a hemispherical bowl is 21 cm. The
made into another solid in the shape of a right
volume of the bowl is equal to: [Take = 22/7]
Y
circular cone of base diameter 10 cm. Find the
, d v¼Zxksykdkj dVksjs dk O;kl 21 lseh gSA dVksjs dkheight of the cone.
vk;ru Kkr dhft,A Øe'k% 10 lseh vkSj 6 lseh ds ckgjh vkSj vkarfjd O;kl ds
( = 22/7 dk iz;ksx dhft,) ,d •ks•ys xksys dks fi?kyk;k tkrk gS vkSj 10 lseh ds vk/
kj O;kl okys ,d yEc o`Ùkh; 'kadq ds vkdkj esa <kydj ,d
(a) 2,425.5 cm3
S
(b) 2,524.5 cm3
H vkSj Bksl cuk;k tkrk gSA 'kadq dh špkbZ Kkr dhft,A
SSC CPO 28/06/2024 (Shift-02)
(c) 2,725.5 cm3 (d) 2,624.5 cm3
(a) 13.68 cm (b) 14.68 cm
37. If the inner radius of a hemispherical bowl is 5 cm
S
and its thickness is 0.25 cm, then find the volume (c) 16.68 cm (d) 15.68 cm
of the material required in making the bowl, [Take 42. A spherical ball of lead, 3 cm in diameter is melted
= 22/7] (Rounded up to two places of decimals) and recast into three spherical balls. The diameters
;fn ,d v/Zxksykdkj dVksjs dh vkarfjd f=kT;k
5 lseh gS vkSj 3
K
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44. A largest possible sphere is carved from a cube of 45. The length of the largest possible rod that can be
side 14 cm. What is its volume in cm3? placed in a cubical room is 423m. The surface
14 lseh Hkqtk ds ,d ?ku ls ,d lcls cM+k laHkkO; xksyk area (in m²) of the largest possible sphere that fit
within the cubical room is:
fudkydj cuk;k tkrk gSA bldk vk;ru lseh3 esa fdruk gS\
[Use = 22/7]
SSC
,d ?kukdkj dejs esa j[kh tk ldus okyh NM+ dh vf/dre
1
(a) 1600 423 ehV
laHkkfor yackbZ j gSA ?kukdkj d{k ds Hkhrj fiQV gksus
3
okys xksys dk vf/dre laHkkfor i`"Bh; {ks=kiQy
2
esa)(eh
D;k
1
(b) 1437 gksxk\
3
SSC CPO 27/06/2024 (Shift-02)
1 (a) 3590
(c) 205
3 (b) 4589
1 (c) 2564
(d) 1707
3 (d) 5544
ANSWER KEY
1. (b) 2. (a) 3. (a) 4. (b) 5. (b) 6. (a) 7. (b) 8. (a) 9. (b) 10. (c)
A
11. (c) 12. (b) 13. (d) 14. (c) 15. (b) 16. (c) 17. (c) 18. (a) 19. (b) 20. (d)
21. (d) 22. (b) 23. (b) 24. (b) 25. (d) 26. (b) 27. (c) 28. (b) 29. (b) 30. (c)
Y
31. (c) 32. (b) 33. (a) 34. (a) 35. (d) 36. (a) 37. (d) 38. (c) 39. (d) 40. (d)
41. (d) 42. (d) 43. (a) 44. (b) 45. (d)
H
S
K
LA
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