Question

The volume of a sphere increases at the rate of 20 cm³ /sec. Find the rate of change of its surface area, when its radius is 5 cm.

Answer 1

Let r be the radius, S be the surface area and V be the volume of the sphere at any time t. 

Then S = 4πr² and V = 4/3 πr³ 

Differentiating w.r.t. t, we get

Hence, the surface area of the sphere is changing at the rate of 8 cm² /sec.