Chapter 13 Surface Areas and Volumes Ex 13.4
Find the surface area of a sphere of radius
(i) 10.5 cm
(ii) 5.6 cm
(iii) 14 cm
(i) We have, r = 105 cm
Find the surface area of a sphere of diameter
(i) 14 cm
(ii) 21 cm
(iii) 3.5 m
Find the total surface area of a hemisphere of radius 10 cm. (Use π = 3.14)
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
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.
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.
Find the radius of a sphere whose surface area is 154 cm2.
Surface area of a sphere = 154 cm2
Hence, the radius of the sphere is 3.5 cm.
The diameter of the Moon is approximately one-fourth of the diameter of the Earth. Find the ratio of their surface areas.
Let diameter of the Earth = d1
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.
Outer radius of the bowl = (Inner radius + Thickness)
= ( 5 + 0.25) cm = 5.25 cm
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).
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