Question

The time rate of change of the radius of a sphere is 1/2π. When it’s radius is 5cm, what will be the rate of change of the surface of the sphere with time?

(a) 10 sq cm

(b) 20 sq cm

(c) 30 sq cm

(d) 40 sq cm

I got this question during an internship interview.

This intriguing question comes from Application of Derivative topic in section Application of Derivatives of Mathematics – Class 12

Answer 1

The correct choice is (b) 20 sq cm

To elaborate: Let, r be the radius and s be the area of the surface of the sphere at time t.

By question, dr/dt = 1/2π

Now, s = 4πr^2;

Thus, ds/dt = 4π * 2r(dr/dt) = 8πr(dr/dt)

When r = 5cm and dr/dt = 1/2π

Then ds/dt = 8π*5*(1/2π) = 20

Thus, correct answer is 20 sq cm.