Volume of sphere of radius $r$ is $V=\frac{4}{3}\pi r^3$

Given $V=288\pi \mathrm{cc}$

$\Rightarrow 288\pi =\frac{4}{3}\pi r^3$

$\Rightarrow r^3=288\times \frac{3}{4}=216$

$\Rightarrow r=6 \mathrm{cm}$.

Again, $V=\frac{4}{3}\pi r^3$

Differentiate w.r.t. '$t$'

$\Rightarrow \frac{dV}{dt}=4\pi r^2\frac{dr}{dt}$

Put the given values, to get

$\Rightarrow 4\pi =4\pi \times 6^2\times \frac{dr}{dt}$

$\Rightarrow \frac{dr}{dt}=\frac{1}{36} \mathrm{cm}/\sec .$