Practice problems for class Mathematics
1. How many litres of milk can a hemispherical bowl of diameter 10.5 cm
hold?
2. 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 g per cm3 ?
3. The diameter of the Moon is approximately one fourth the diameter of
the Earth. What fraction is the volume of the Moon of the volume of the Earth?
4. A hemispherical tank is made up of an iron sheet 1 cm thick. If the
inner radius is 1m, then find the volume of the iron used to make the tank.
5. Find the volume of a sphere whose surface area is 154 cm2.
6. A dome of a building is in the form of a hemisphere. From inside, it
was white washed at the cost of Rs 498.96. If the rate of white wash is Rs 2.00
per square meter, find
(i) inside surface area of the dome, (ii) the volume of the air inside
the dome.
7. A hemispherical bowl of steel is of thickness 0.3 cm . If
the inner radius of the bowl is 7 cm, find the volume of the steel used in
making the bowl.
8. The volume of a conical tent is 1232 m3 and the area of its base is 154
m2.Find the length of the canvas required to build the tent, if the canvas is 2
m in width.
9. A cylindrical bucket, 14 cm in radius, is filled with water to some
height. If a rectangular solid of size 28 cm ×11 cm × 10 cm is immersed
in the water, find theheight by which water rises in the bucket.
10. A 11 cm × 4 cm rectangular piece of paper is folded and taped without
overlapping to make a cylinder of height 4 cm. Find the volume of the cylinder
so formed.
11. A conical pit of top diameter 3.5 m is 12 m deep. What is its
capacity in kilolitres?
12. The volume of a right circular cone is 9856 cm3. If the diameter of the
base is 28 cm, find (i) height of the cone,(ii) slant height of the cone,(iii)
curved surface area of the cone.
13. A conical tent is 9 m high with base diameter 24 m. Find the number
of persons it can accommodate if each person requires
(i) 2 m2 space on
the ground,
(ii) 15 m3space to breathe,
(iii) 2 m2 space on the round and 15 m3
space to breathe.
14. A right triangle ABC with its sides 5 cm, 12 cm and13 cm is revolved about
the side 12 cm. Find the volume of the solid so obtained
15.If the triangle ABC with its sides 5 cm, 12 cm and13 cm is revolved about the side 5 cm,
then find the volume of the solid so obtained. Find also the ratio of
the volumes of the two solids obtaine
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