X Maths gb
1
AJAY PARMAR
GROUP TUITION
Chapter:14 surface area and volume
Section – 1
1. The volume of the sphere with diameter 1 cm is … cm3.
(a)
2

3
(b)
1

6
(c)
1

24
(d)
4

3
2. The volume of hemisphere with radius 1.2 cm is … cm3.
(a) 1.152
(b) 0.96
3. The volume of sphere is
(c) 2.152
(d) 3.456
4
 cm3. Then its diameter is … cm.
3
(a) 0.5
(b) 1
(c) 2
4. The volume of cone with radius 2 cm and height 6 cm is … cm3.
(d) 2.5
(a) 8
(b) 12
(c) 14
(d) 16
5. The diameter of the base of the cone is 10 cm and its slant height is 17 cm. Then the curved surface area of
the cone is … cm2.
(a) 85
(b) 170
(c) 95
(d) 88
6. The diameter and the height of the cylinder are 14 cm and 10 cm respectively. Then the total surface is …
cm2.
(a) 44
(b) 308
(c) 748
(d) 1010
7. The ratio of the radii of two cones having equal height is 2 : 3. Then, the ratio of their volumes is … .
(a) 4 : 6
(b) 8 : 27
(c) 3 : 2
(d) 4 : 9
8. If the radii of a frustum of a cone are 7 cm and 3 cm and the height is 3 cm, then the curved surface area is
… cm2.
(a) 50
(b) 25
(c) 35
(d) 63
9. The radii of a frustum of a cone are 5 cm and 9 cm and height is 6 cm, then the volume is … cm3.
(a) 320
(b) 151
(C) 302
(d) 98
10. The formula to find total surface area of a solid formed by a cylinder with both ends enclosed by
cones is ___.
(a) rh + r2
(b) 2r(h + l)
(c) r(l + r)
(d) 2r(l + r)
11. The formula to find volume of a solid formed by a cylinder with both ends enclosed by hemispheres
is ___.
(a) 2r(h + l)
(b) 2(2/3r2h)
(c) r2(h + 4/3r)
(d) 1/3r2(h + 2r)
12. For a cylinder if the radius is doubled and the height is halved then its volume becomes ___ times
its original volume.
(a) 2
(b) 8
(c) 1/8
13. The radius of a sphere is 5 cm. Its curved surface area is ____ cm2.
(a) 200
(b) 100
(c) 10
14. The formula of find the volume of a 1 rupee coin is ____.
(d) ½
(d) 20
(a) 1/3 r2h
(b) 4/3  r3
(c)  r2h
(d) 2 rh
15. The heights of two cylinders are equal. The radius of first cylinder is ½ that of the second. The
volume of second cylinder is ____ times the first cylinder.
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X Maths gb
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AJAY PARMAR
GROUP TUITION
Chapter:14 surface area and volume
(a) 8
(b) 16
(c) 4
3
16. 1 l = ____ m .
(a) 102
(b) 103
(c) 10–2
17. What is the volume of a sphere if its radius is 1.5 cm?
(d) 2
(d) 10–3
(a) 1.5 cm3
(b) 0.5 cm3
(c) 3 cm3
(d) 4.5 cm3
18. The ratio of radii of two cylinders with equal heights is 2 : 3. Find the ratio of their volumes.
(a) 2:3
(b) 3:2
(c) 4:9
(d) 8:27
19. The curved surface area of a sphere is half of its volume. Find the radius of the sphere.
(a) 3
(b) 6
(c) 9
(d) None of these
20. How many liters of milk can be stored in a cylindrical tank radius 140 cm and height 3 m?
(a) 48180
(b) 14840
(c) 18480
(d) 10848
21. The total surface of area of each part of a sphere, with radius 1cm, divided into four equal parts is ___cm2.
(a) 
(b) 2
(c) 3
(d) 4
22. The total surface area of a hollow hemisphere with outer radius R and inner radius of r is ___.
(a) 2(R2 + r2)
(b) 2(R2 − r2)
(c) (3R2 + r2)
(d) 3(R2 + r2)
23. The total outer surface area of a hollow cylinder of height h with outer radius R and inner radius of r is ___.
(a) 2Rh
(b) 2rh
(c) 2h(R + r)
(d) 2(Rh + r2)
24. The curved surface area of a cone 550 cm2. If its diameter is 14 cm, find its vertical height.
(a) 25cm
(b) 7cm
(c) 24cm
(d) 15cm
3
25. Volume of a hemisphere is 523.908 m . The diameter of the hemisphere is ___.
(a) 63m
(b) 6.3m
(c) 630cm
(d) 1260cm
Section – 2
A Solve the following (2 marks each)
10
1. A cylinder has hemispherical ends on both sides. If the total height and the diameter of the solid are 78 cm,
and 28 respectively then find the total surface area of the solid.
2. The radius and height of a conical dome of a temple is 7m and 24 m respectively. Find the cost of painting
3.
4.
5.
B
is inner and outer surface at the rate of `. 15 per sq m.
The diameter of a circular plot is 5.6 m. How much soil is required to raise level of the ground by 25 cm?
How many balls of diameter 1 cm can be prepared by melting a metal cylinder of radius 5 cm and height 7
cm?
If the difference between the two diameters of a frustum is 24 cm and its slant height is 15 cm then find the
height of the frustum.
Solve the following (3 marks each)
6
6. A tent is made of a cone mounted on a hollow cylinder. If the diameter and height of the cylinder are 24m
and 11 m and slant height of the cone is 13 m then find the total surface area of the canvass used in making
the tent.
7. A playing top is made up of steel. The top is shaped like a cone surmounted by a hemisphere. The total
height of top is 5 cm and the diameter of the top is 3.5 cm. Find the volume of the top.
C Solve the following (4 marks each)
4
8. The total surface area of a solid composed of a cone mounted on a hemisphere is 361.1 cm2. If the slant
height of the conical part is 13 cm then find the total height of the solid.
D Solve the following (5 marks each)
5
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X Maths gb
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AJAY PARMAR
GROUP TUITION
Chapter:14 surface area and volume
9. An open metal bucket is in the shape of a frustum of a cone, mounted on a hollow cylindrical base made of
the same metallic sheet. The total vertical height of the bucket is 40 cm and that of cylindrical base is 10 cm,
radii of two circular ends are 60 cm and 20 cm. Find the area of the metallic sheet used. Also find the
volume of water the bucket can hold? ( = 3.14)
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AJAY PARMAR
GROUP TUITION
Chapter:14 surface area and volume
Answers:
Section-1
1. B
2. A
3. C
4. A
5. A
6. C
7. D
8. A
9. C
10. B
11. C
12. A
13. B
14. C
15. C
16. D
17. D
18. C
19. B
20. C
21. B
22. C
23. C
24. C
25. D
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Gurukul
X Maths gb
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AJAY PARMAR
GROUP TUITION
Chapter:14 surface area and volume
Section-2
1.
Refer Text book example 2
2.
Refer Text book example 6
3.
Refer Text book example 11
4.
Refer Text book example 14
5.
h = 9 cm
6.
Refer Text book example 3
7.
Refer Resources Ex 14.2, Q. 6
8.
Refer Text book example 7
9.
Refer Resources Ex 14.4, Q. 1
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