The volume of a sphere is increasing at the rate of $4\pi cc/\sec$ when its volume is $288\pi cc$, the rate of increase (in cm/sec) in its radius is

$\begin{array}{l}v=288\pi \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\frac{dv}{dt}=4\pi \\ \frac{4}{3}\pi r^3=288\pi \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em} \frac{d}{dt}\left(\frac{4}{3}\pi r^3\right)=4\pi \\ r^3=72\times 3\hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\hspace{0.25em} r^2\frac{dr}{dt}=1\\ r=6\hspace{0.25em} \hspace{0.25em}\hspace{0.25em}\hspace{0.25em}\frac{dr}{dt}=\frac{1}{36}\end{array}$