If the volume of a sphere increase at the rate of 2π cm³/sec, then the rate of increase of its radius (in cm/sec), when the volume is 288π cm³.

1/72

If r is the radius of a sphere at the time t then its volume $V=\frac{4}{3}πr^3$

$V=288π⇒\frac{4}{3}πr^3=288π⇒r^3=216⇒r=6$

$V=\frac{4}{3}πr^3⇒\frac{dV}{dt}=4πr^2\frac{dr}{dt}⇒2π=4π(6)^2\frac{dr}{dt}⇒\frac{dr}{dt}=\frac{1}{72}$