NCERT Solutions for Class 9th Mathematics
Chapter 13. Surface Areas and Volumes
Assume π = , unless stated otherwise.
1. Find the volume of a sphere whose radius is
(i) 7 cm (ii) 0.63 m
2. Find the amount of water displaced by a solid spherical ball of diameter
(i) 28 cm (ii) 0.21 m
3. 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 ?
4. The diameter of the moon is approximately one-fourth of the diameter of the earth. What fraction of the volume of the earth is the volume of the moon?
Let diameter of earth = x
5. How many litres of milk can a hemispherical bowl of diameter 10.5 cm hold?
Diameter = 10.5 , radius = 5.25
6. A hemispherical tank is made up of an iron sheet 1 cm thick. If the inner radius is 1 m, then find the volume of the iron used to make the tank.
Radius = 1.01 m , radius = 1 m
7. Find the volume of a sphere whose surface area is 154 cm2.
Surface area = 154 cm2
8. A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of 498.96. If the cost of white-washing is 2.00 per square metre, find the
(i) inside surface area of the dome, (ii) volume of the air inside the dome.
9. Twenty seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S2. Find the
(i) radius r2 of the new sphere, (ii) ratio of S and S2.
R = r
10. A capsule of medicine is in the shape of a sphere of diameter 3.5 mm. How much medicine (in mm3) is needed to fill this capsule?
Diameter = 3.5 mm , r = 1.75 mm