Surface Areas and Volumes – Exercise 13.8 – (MATHEMATICS) – 9th Class
Assume π =, unless stated otherwiese.
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?
5. How many liters milk can a hemispherical bowl of diameter 10.5 cm hold?
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.
7. Find the volume of a sphere whose surface area is 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 Rs.498.96. If the cost of white-washing is Rs.2.00 per square metre, find the
(i) inside surface area of the dome,
(ii) volume of the air inside the dome. Sol. Cost of white washing = 498.96. Rate of white-washing = 2 per sq. m.
Sol. Cost of white washing = 498.96. Rate of white-washing = 2 per sq. m.
9. Twenty seven solid iron spheres, each of radius r and surface area S are melted to form a sphere with surface area S’. Find the
(i) radius r’ of the new sphere,
(ii) ratio of S and S’
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?