Chapter 13 Surface Areas and Volumes Ex 13.4 eng

Chapter 13 Surface Areas and Volumes Ex 13.4

Question 1.
Find the surface area of a sphere of radius
(i) 10.5 cm
(ii) 5.6 cm
(iii) 14 cm
Solution:
(i) We have, r = 105 cm

Question 2.
Find the surface area of a sphere of diameter
(i) 14 cm
(ii) 21 cm
(iii) 3.5 m
Solution:

Question 3.
Find the total surface area of a hemisphere of radius 10 cm. (Use π = 3.14)
Solution:
We have, r = 10 cm
Total surface area of a hemisphere = 3πr²
= 3 x 3.14 x (10)²
= 9.42 x 100
= 942 cm²

Question 4.
The radius of a spherical balloon increases from 7 cm to 14 cm as air is being pumped into it. Find the ratio of surface areas of the balloon in the two cases.
Solution:

Question 5.
A hemispherical bowl made of brass has inner diameter 10.5 cm. Find the cost of tin-plating it on the inside at the rate of ₹16 per 100 cm².
Solution:

Question 6.
Find the radius of a sphere whose surface area is 154 cm².
Solution:
Surface area of a sphere = 154 cm²

Hence, the radius of the sphere is 3.5 cm.

Question 7.
The diameter of the Moon is approximately one-fourth of the diameter of the Earth. Find the ratio of their surface areas.
Solution:
Let diameter of the Earth = d₁

Question 8.
A hemispherical bowl is made of steel, 0.25 cm thick. The inner radius of the bowl is 5 cm. Find the outer curved surface area of the bowl.
Solution:
Outer radius of the bowl = (Inner radius + Thickness)
= ( 5 + 0.25) cm = 5.25 cm

Question 9.
A right circular cylinder just encloses a sphere of radius r (see figure). Find
(i) surface area of the sphere,
(ii) curved surface area of the cylinder,
(iii) ratio of the areas obtained in (i) and (ii).
Solution:

The radius of the sphere = r
Radius of the cylinder = Radius of the sphere = r
Height of the cylinder = Diameter = 2r
(i) Surface area of the sphere A₁ = 4πr²
(ii) Curved surface area of the cylinder = 2πrh
A₂ = 2π x r x 2r
A₂ = 4πr²
(iii) Required ratio = A₁ :A₂ = 4πr² : 4πr² = 1 : 1