A right circular cylinder just encloses a sphere of radius r (see fig. 13.22). 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:

(i) Surface area of sphere = 4πr2, where r is the radius of sphere

(ii) Height of cylinder, h = r+r =2r

Radius of cylinder = r

CSA of cylinder formula = 2πrh = 2πr(2r) (using value of h)

= 4πr2

(iii) Ratio between areas = (Surface area of sphere)/(CSA of Cylinder)

= 4πr2/4πr2 = 1/1

Ratio of the areas obtained in (i) and (ii) is 1:1.