Answer
$ 4860 $ $\frac {cm^ {3}} {min}$
Work Step by Step
Let $V$ and $r$ denote volume and radius respectively, then:
$ V=\frac {4}{3} \pi r^3$
$ \frac{dV}{dt}=\frac {d (\frac {4}{3} \pi r^3)} {dr} \frac{dr}{dt}=\frac {4}{3} \pi \frac{d(r^3)} {dr} \frac{dr}{dt}$
$ \frac{dV}{dt}= \frac {4}{3} \pi (3r^2) \frac{dr}{dt}=4\pi r^ {2} \frac{dr}{dt}$............... eq (1)
Putting $\frac{dr}{dt}=15 \frac{cm}{min}$ $r=9 cm$ in equation (1)
$ \frac{dV}{dt}=4\pi (9^ {2}) \times 15=4860$ $\frac {cm^ {2}} {min}$
