Question

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).

Answer 1

(i) Surface area of sphere = 4πr²

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

Radius of cylinder = r

CSA of cylinder = 2πrh

= 2πr (2r)

= 4πr²

(iii)

Therefore, the ratio between these two surface areas is 1:1.