Question

The radius of a sphere is increasing at the rate of 0.2 cm/sec. The rate at which the volume of the sphere increases when radius is 15 cm, is

A. 12π cm³/sec

B. 180π cm³/sec

C. 225π cm³/sec

D. 3π cm³/sec

Answer 1

Correct answer is B.

The volume of a sphere, of radius r, is defined by

V(r) = \(\frac{4}{3}πr^3-(1)\)

Given that r = 15cm, \(\frac{dr}{dt} = 0.2\, cm/sec,\) we have to calculate \(\frac{dV}{dt}\)

Differentiating (1) with respect to t, we get

\(\frac{dV}{dt}\) = 4πr²\(\frac{dr}{dt}\)

Substituting values, we get