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SURFACE AREAS AND VOLUMES
1. The volume of right circular cone of height 12 cm, and base radius 6cm is
a. b. c. d.
12 Ο ππ
3
36 Ο ππ
3
72 Ο ππ
3
144 Ο ππ
3
2. If the height of a cone is doubled then its volume is increased by
a. 100% b. 200% c. 300% d. 400%
3. The volume of a sphere, if radius is 10.5 cm
a. 9702cm
3
b. 4851cm
3
c. 19404cm
3
d. 14553cm
3
4. Volume of sphere whose radius is 7 cm is
a. 1437.33 cm
3
b. 0.0143733 cm
3
c. 1.43733 d.
None of the above
5. In the class intervals 10-20, 20-30, the number 20 is included in
a. 10-20 b. 20-30 c. Both of the intervals d. None of
these
6. If the radius of a sphere is doubled, then what is the ratio of their surface area?
a. 1:2 b. 2:1 c. 1:4 d. 4:1
7. If a right circular cone has radius 4 cm and slant height 5 cm then what is its volume?
a. b. c. d.
16 Ο ππ
3
14 Ο ππ
3
12 Ο ππ
3
18 Ο ππ
3
8. A cuboid is 12cm long, 9 cm broad and 8cm height, find its total surface area.
9. The volume of a cube is 512cm
3
. Find its total surface area.
10. Find the length of the longest rod that can fit in a cubical vessel of side 10 cm.
11. Find the volume of a sphere having radius 2r.
12. FInd the volume of a sphere whose surface area is 154 cm
2
.
13. If the volume of a right circular cone of height 9cm is 48 cm
3
, Find the diameter of the
Ο
base.
14. The volume of two spheres are in the ratio 64:27. Find the ratio of their surface area.
15. A cone of height 8 m has a curved surface area 188.4 m
2
. Find its volume . (
Take =3.14)
Ο
16. A hemispherical dome of a building needs to be painted. If the circumference of the base
of the dome is 17.6m, find the cost of painting it, given the cost of painting is Rs. 5 per
100 cm
2
.
17. The radius and height of a cone are in the ratio 4:3. The area of the base is 154cm
2
.
Find the area of the curved surface area.
18. A sphere, cylinder and cone are of the same radius and same height. Find the ratio of
their curved surfaces area?
19. The volume of a right circular cone is 9856 cm
3
. If the diameter of the base is 28 cm,
find
a. Height of the cone
b. Slant height of the cone
c. Curved surface area of the cone
20. A soft drink is available in two packs β
a. a tin can with a rectangular base of length 5 cm and width 4 cm, having a height
of 15 cm and
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b. a plastic cylinder with circular base of diameter 7 cm and height 10 cm.
Which container has greater capacity and by how much?
21. The volume of a right circular cone is 9856 cm
3
. If the diameter of the base is 28 cm.
Find :-
a. Height of the cone.
b. Slant height of the cone
c. Curved surface area of cone
22. How many meters of cloth 5 m wide will be required to make a conical tent the radius of
whose base is 7 m and height is 24 m?
23. A conical tent is to accommodate 11 persons, each person must have 4 m
2
of the space
on the ground and 20 m
3
of air to breathe. Find the height of the tent.
24. The volume of two spheres are in the ratio 64:27. Find the ratio of their surface areas.
25. Volume and surface area of a solid hemisphere are numerically equal. What is the
diameter of the hemisphere?
26. Find the surface area of a sphere whose volume is 4851 m
3
.
27. On increasing the radius of a sphere by 10%. Find percentage increase in its volume.
28. Find the total surface area of a cone if its slant height is 21 m and diameter of its base is
24 m.
29. A dome of a building is in the form of a hemisphere fro inside it was white washed at the
cost of Rs 4689.60. If the cost of white washing is Rs 20 per m
2
. Find the:-
a. Inside surface area of the dom
b. Volume of the air inside the dome.
30. The diameter of the moon is approximately one-fourth of the diameter of the earth. Find
:-
a. The ratio of the earth is the volume of the moon
b. Ratio of their surface area
31. The diameter of a metallic ball is 4.2 cm . What is the mass of the ball if the density of
the metal is 8.9 gm per cm
3
32. A conical tent is 10 m high and the radius of its base is 24 m. Find
a. slant height of the tent.
b. cost of the canvas required to make the tent, if the cost of 1 m2 canvas is Rs 70.
33. The slant height and base diameter of a conical tomb are 25 m and 14 m respectively.
Find the cost of white-washing its curved surface at the rate of rupees 210 per 100 m
2
.
34. A cone of height 8 m has a curved surface area 188.4 m
2
. Find its volume. (
Ο= 314 )
35. A sphere of diameter 12.6 cm is melted and cast into a right circular cone of height 25.2
cm. Find the radius of the base of the cone.
36. Mr. Kumar, a Mathematics teacher, brings some green coloured clay in the classroom to
teach the topic βmenstruationβ. First, he forms a cylinder of radius 6 cm and height 8 cm
with the clay. Then, he moulds that cylinder into a sphere similarly, he moulds the sphere
in other different shapes. Answer the following questions.
a. Which of the following is not a 3D shape?
i. Cone ii. Cuboid iii. Rectangle iv. Sphere
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b. What is the volume of the cylindrical shape?
i. ii. iii. iv.
268 Ο ππ
3
288 Ο ππ
3
36 Ο ππ
3
48 Ο ππ
3
c. When clay changes from one shape to another, which of the following remains
the same.
i. Volume ii. Area iii. CSA iv. Radius
d. The radius of the sphere formed is:
i. 4cm ii. 5cm iii. 6cm iv. 3cm
