Chapter 13 Surface Areas and Volumes Ex 13.8 eng

Chapter 13 Surface Areas and Volumes Ex 13.8

Question 1.
Find the volume of a sphere whose radius is
(i) 7 cm
(ii) 0.63 cm
Solution:
(i) We have, r = 7 cm

Question 2.
Find the amount of water displaced by a solid spherical ball of diameter
(i) 28 cm
(ii) 0.21 m
Solution:
(i) We have, d = 28 cm
⇒ r = 14 cm

Question 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:
We have, d = 4.2 cm ⇒ r = 2.1 cm

The density of the metal per cm³ = 8.9 g
The density of the metal 38.808 cm³ = 38.808 x 8.9 g = 345.39 g
Hence, the mass of the ball = 345.39 g

Question 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:

Question 5.
How many litres of milk can a hemispherical bowl of diameter 10.5 cm hold?
Solution:
Diameter = 10.5 cm
⇒ Radius, r = 5.25 cm

Question 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.
Solution:
Inner radius (r₁) = 1 m -100 cm
Outer radius (r₂) = (100 + 1)cm ( ∵ Inner radius + Thickness)
= 101 cm

Question 7.
Find the volume of a sphere whose surface area is 154 cm².
Solution:
We have, surface area of a sphere = 154 cm²

Question 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.
Solution:
Cost of white washed = ₹ 498.96
Cost of white washing per square metre = ₹ 2.00

Question 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’.
Solution:

Question 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?
Solution:
We have, diameter = 3.5 mm