SURFACE AREA AND VOLUME
EXERCISE 13.8
EXERCISE 13.8
Q 1. Find the volume of a sphere whose radius is
(i) 7 cm (ii) 0.63 m
Solution: (i) Here, radius (r) = 7 cm
Q 2. Find the amount of water displaced by a solid spherical ball of diameter
(i) 28 cm (ii) 0.21 m
Solution: (i) Diameter of the ball = 28 cm
Q 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?
Solution: Diameter of the metallic ball = 4.2 cm
Q 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?
Solution: Let diameter of the earth be 2r.
Q 5. How many litres of milk can a hemispherical bowl of diameter 10.5 cm hold?
Solution: Diameter of the hemisphere = 10.5 cm
Q 6. A hemispherical tank is made up of an iron sheet 1 then find the volume of the iron used to make the tank.
Solution: Inner radius (r) = 1m
Q 7. Find the volume of a sphere whose surface area is 154 cm2
Solution: Let ‘r’ be the radius of the sphere.
Its surface area = 4πr2
Q 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.
Solution: Total cost of white washing = Rs. 498.96
Rate of white washing = Rs. 2 per m
(i) To find the inside surface area of the dome:
∵Radius of the hemisphere (r) = 6.3 m
Surface area of a hemisphere = 2πr2 m2
Thus, the required surface area of the dome = 249.48 m2
(ii) To find the volume of air in the dome:
Thus, the required volume of air inside the dome is 523.9 m3 (approx.).
Q 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 sphere, (ii) ratio of S and S’.
Soutionl: (i) To find r’:
∵Radius of a small sphere = r
Solution: Diameter of the spherical capsule = 3.5 mm
