PRISM PYRAMID

PRISM/PYRAMID/
TETRAHEDRON/FRUSTUM

PRISM/PYRAMID/FRUSTUM TETRAHEDRON

PRISM

Volume = base Area × h Volume = a3 2
CSA = base perimeter × h 12
TSA = CSA + 2 × base Area
TSA = a2 3
PYRAMID
FRUSTUM

Volume = 1 × base Area × h  Volume= 13 r12  r22  r1r2 h
3
CSA = r1  r21
TSA = CSA + Base Area
  TSA =  r1  r2 1  r12  r22
1
Slant height =  r1 r2 2 h2
\

1. A right prism with trapezium base of parallel 6. Base of a prism is an equilateral triangle and

sides 8 cm and 14 cm and height of prism is 12 its area 173 cm2 and volume is 10380 cm3.

cm and volume of prism is 1056 cm3 then find Then find its CSA ? ( 3 = 1.73).
distance b/w two parallel sides.

(A) 3450 (B) 3560

(A) 6 cm (B) 8 cm (C) 3600 (D) 3850

(C) 7 cm (D) 10 cm 7. The height of prism with square base is 15 cm.

2. A right prism stand on a base of 6 cm side If total surface area of prism is 608 cm2. Find
equilateral triangle and its height is 9 cm. Find its volume.

volume of prism.

(A) 64 3 cm2 (B) 56 3 cm2 (A) 960 (B) 860

(C) 750 (D) 865

(C) 76 3 cm2 (D) 81 3 cm2 8. The altitude of a prism is 10 cm and its base is

3. The perimeter of triangular base prism is 15 an regular hexagon of side 12 cm find its TSA.

cm and radius of in circle of triangular of

triangular base is 3 cm. If volume of prism be

270 cm3 then find height of prism.

(A) 144 (5 + 3 ) (B) 132 (7 + 3 )

(A) 10 cm (B) 11 cm (C) 156 (3+ 3 ) (D) None of these

(C) 12 cm (D) 15 cm 9. A prism has the base of right angle triangle

4. Find CSA and TSA of a prism which is based on whose sides adjacent to right angle are 10 cm

a triangle of perimeter 45 cm and in circle and 12 cm. The height of prism is 12 cm. The

radius 9 cm and its volume is 810 cm3. density of material of prism is 60gm/cm3. What

is the weight of prism.

s

(A) 180, 585 (B) 180, 485 (A) 5.6 kg (B) 6.4 kg

(C) 260, 582 (D) 260, 45 (C) 6.8 kg (D) 7.2 kg

5. The base of a prism is a triangle whose sides 10. The base of a right pyramid is a square of side
are 9cm, 12cm, 15cm and the height of prism
40 cm long. The volume of pyramid is 8000
is 5 cm. Find its TSA.
cm3. Find its height.

(A) 285 cm2 (B) 288 cm2 (A) 12 cm (B) 14 cm
(C) 275 cm2 (D) 296 cm2 (C) 15 cm (D) 18 cm

2

11. The base of a right pyramid is a hexagon of 16. If length of each side of regular tetrahedron is

side 15 cm and its height is 12 cm. Find its 12 cm. Then find its volume and TSA.

volume. 12 cm

(A) 1350 3 (B) 1250 3 (A) 144 2 , 144 3 (B) 144 3 , 144 2

(C) 1150 3 (D) 1550 3 (C) 96 2 ,96 3 (D) 96 3 , 96 2

17. If volume of sphere, cube, tetrahedron, and

12. The base of pyramid is a square of side 16 cm. octahedron be same then which has maximum

If height is 15 cm. Find its CSA and TSA. surface area.

(A) Sphere (B) Cube

(A) 544, 800 (B) 544, 750 (C) Tetrahedron (D) Octahedron

(C) 534, 960 (D) 574, 640 18. If radius of circular ends of the circular ends of

13. A rectangle base pyramid whose base length bucket which is 45 cm high are 28 cm and 7
18 cm and breath 10 cm. Find its TSA. If it's cm find capacity of bucket.

height is 12 cm.

(A) 48510 cm3 (B) 46820 cm3

(C) 36250 cm3 (D) 39260 cm3

(A) 564 (B) 546 19. Find the CSA of a frustum if slant height of

(C) 576 (D) 596 the frustum of cone is 4 cm and the perimeter

14. The base of a pyramid is an equilateral triangle of its circular bases are 18 cm and 6 cm.

of side 10 3 cm if its TSA 270 3 cm2 find
its height.

10 3 cm (A) 44 cm2 (B) 48 cm2

270 3 cm2 (C) 52 cm2 (D) 62 cm2

(A) 5 cm (B) 8 cm 20. A bucket in the form of frustum of cone and
(C) 10 cm (D) 12 cm hold 28.490 lit water. The radius of top and
bottom are 28 cm and 21 cm find height of
bucket.

15. There is a pyramid on base which is a regular
hexagon of side ‘2a’ cm if every slant edge of

pyramid is 5a cm find its volume.
2
(A) 15 cm (B) 12 cm

'2a' cm (C) 16 cm (D) 18 cm

5a cm 21. A tent is made in the form of conic frustum
2 surrounded by a cone. The diameter of base and
top of frustum 20 m and 6 m and height is 24
m. It height of tent 28 m.

(A) 3 3 a3 (B) 4 3 a3 Find quantity of canvas required.

(C) 5 3 a3 (D) 6 3 a3

3

CGL Mains 2018

(A) 340 m2
(B) 320 m2
(C) 330 m2
(D) 350 m2

PREVIOUS YEARS (A) 48[( 3 ) + 1] (B) 24[4 + ( 3 )]
QUESTIONS

(C) 28[6 + ( 3 )] (D) 32[3 + ( 3 )]

22. A right prism has a square base with side of 24. A regular hexagonal base prism has height 8

base 4 cm and the height of prism is 9 cm. The cm and side of base is 4 cm. What is the total

prism is cut in three parts of equal heights by surface area (in cm2) of the prism?
two planes parallel to its base. What is the ra-

tio of the volume of the top, middle and the 8

bottom part respectively? 4

4 2
9
CGL Mains 2018

(A) 54(3 + 3 ) (B) 36(3 + 3 )

(C) 48(4 + 3 ) (D) 24(4 + 3 )

CGL Mains 2018 25. A regular square pyramid has side of its base

(A) 1 : 8 : 27 (B) 1 : 7 : 19 20 cm and height 45 cm is melted and recast

(C) 1 : 8 : 20 (D) 1 : 7 : 20 into regular triangular pyramids of equilateral
base of side 10 cm and height 10 3 cm. What
23. A right triangular pyramid XYZB is cut from cube are total numbers of regular triangular pyra-
as shown in figure. The side of cube is 16 cm. X,

Y and Z are mid points of the edges of the cube. mid?

What is the total surface area (in cm2) of the 20
pyramid?

45

XYZB 10 10 3
16 X, Y Z

2

4

CGL Mains 2018

(A) 24 (B) 20 CGL Mains 2018

(C) 27 (D) 28 (A) 3 3 (B) 6 3

26. A right triangular prism has equilateral triangle (C) 6 (D) 3

as its base. Side of the triangle is 15 cm. Height 29. A regular pyramid has a square base. The height

of the prism is 20 3 cm. What is the volume of the pyramid is 22 cm and side of its base is

(in cm3) of the prism? 14 cm. Volume of pyramid is equal to the vol-

ume of a sphere. What is the radius (in cm) of

the sphere?
15 20 3

3 22 14

CGL Mains 2018

(A) 1125 (B) 6750

(C) 4500 (D) 3375 CGL Mains 2018

27. A regular triangular pyramid is cut by 2 planes (A) 3 49 (B) 7
which are parallel to its base. The planes tri-

sects the altitude of the pyramid. Volume of (C) 14 (D) 3 98

top, middle and bottom parts is V1, V2 and V3 30. The base of a prism is in the shape of an equi-
respectively. What is the value of V1 : V2 : V3 ? lateral 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 cm3) of the prism?

V1, V2 V3 V1 18 20

: V2 : V3 3
(A) 1 : 8 : 27
CGL Mains 2018 CGL Mains 2018
(B) 1 : 8 : 19

(C) 2 : 9 : 27 (D) 1 : 7 : 19 (A) 60 3 (B) 30 6

28. A prism has a regular hexagonal base with side (C) 60 2 (D) 120 3
6 cm. If the total surface area of prism is 216 3

31. A pyramid has a square base. The side of square
cm2, then what is the height (in cm) of prism? is 12 cm and height of pyramid is 21 cm. The

6 pyramid is cut into 3 parts by 2 cuts parallel to

216 3 2 its base. The cuts are at height of 7 cm and 14

5

cm respectively from the base. What is the dif- (A) 64 ( 17 + 1) CGL Mains 2018
ference (in cm3) in the volume of top most and (B) 32( 13 + 1)
bottom most part?

21 12 (C) 64 ( 3 + 1) (D) 32( 5 +1)
2 34.
3 The base of right prism is a trapezium whose
7 14 parallel sides are 11 cm and 15 cm and the dis-
tance between them is 9 cm. If the volume of
3 the prism is 1731.6 cm3, then the height (in
cm) of the prism will be:

CGL Mains 2018

(A) 872 (B) 944 11 15
9 1731.6
(C) 786 (D) 918

32. A prism has a square base whose sides is 8 cm. (A) 15.2 CGL Mains 2019
The height of prism is 80 cm. The prism is cut (C) 14.8 (B) 14.2
into 10 identical parts by 9 cuts which are par- (D) 15.6
allel to base of prism. What is the total surface
area (in cm2) of all the 10 parts together?

8 35. The volume of a right pyramid is  3 cm3 and
its base is an equilateral triangle with side 6
80 cm. What is the height (in cm) of the pyramid?

9 10 10

2 (Right pyramid)

CGL Mains 2018  3 3

(A) 4260 (B) 2560 6

(C) 3840 (D) 3220

33. A pyramid has a square base, whose side is 8 CGL Mains 2019

cm. If the height of pyramid is 16 cm, then what (A) 20 (B) 15

is the total surface area (in cm2) of the pyra- (C) 12 (D) 18

mid? 36. The base of a right prism is a triangle with sides
20 cm, 21 cm and 29 cm. If its volumeis 7560
8 cm3, then its lateral surface area (in cm2) is :

16 20
7560
2

21 29

6

3 of the cone?

(A) 2556 CGL Mains 2019 (Take  = 3.14) 5
(C) 2448 (B) 2484 : 12
(D) 2520 816.4

37. The base of a right pyramid is an equilateral 3  = 3.14
triangle with side 8 cm, and the height of the
pyramid is 24 3 cm. The volume (in cm3) of the (A) 1256 CGL Mains 2019
pyramid is: (B) 3140

8 (C) 628 (D) 2512

24 3 39. A right prism has height 18 cm and its base is a
triangle with sides 5 cm, 8 cm and 12 cm. What
3 is its lateral surface area (in cm2)?

(A) 480 CGL Mains 2019 18 8 12
(B) 384 5

(C) 576 (D) 1152

38. The radius and the height of a right circular (A) 450 CGL Mains 2019
cone are in the ratio 5 : 12. Its curved surface (C) 486
area is 816.4 cm2. What is the volume (in cm3) (B) 468
(D) 432

ANSWER KEY

1. (B) 6. (C) 11. (A) 16. (B) 21. (A) 26. (D) 31. (*) 36. (D)
2. (D) 7. (A) 12. (A) 17. (C) 22. (*) 27. (D) 32. (C) 37. (B)
3. (C) 8. (A) 13. (A) 18. (A) 23. (D) 28. (A) 33. (A) 38. (D)
4. (A) 9. (D) 14. (D) 19. (B) 24. (C) 29. (B) 34. (C) 39. (A)
5. (B) 10. (C) 15. (A) 20. (A) 25. (A) 30. (*) 35. (B)

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