Question

The surface area of a spherical balloon is increasing at the rate of 2 cm² /sec. At what rate is the volume of the balloon is increasing, when the radius of the balloon is 6 cm?

Answer 1

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

Then S = 4πr² and V = 4/3 πr³ 

Differentiating w.r.t. t, we get

Hence, the volume of the spherical balloon is increasing at the rate of 6 cm³ / sec.