Answer
$16800\pi\,cm^{2}/min $
Work Step by Step
Surface area, $ S=4\pi r^{2}$
$\frac{dS}{dt}=\frac{dS}{dr}\times\frac{dr}{dt}=\frac{d}{dr}(4\pi r^{2})\times30\,cm/min $
$=8\pi r\times30\,cm/min $
As r=10 at t=0 and $\frac{dr}{dt}=30\,cm/min $, $ r=(10+2\times30) cm= 70 cm $ at t= 2 min.
Then,
$\frac{dS}{dt}=8\pi(70\,cm)\times30\,cm/min $$=16800\pi\,cm^{2}/min $
