Answer
$9600\pi\,cm^{2}/min $
Work Step by Step
We know that the surface area of a sphere is given by:
$S=4\pi r^2$
We can find the rate of change of the surface area with respect to time as:
$\frac{dS}{dt}=\frac{dS}{dr}\times\frac{dr}{dt}=\frac{d}{dr}(4\pi r^{2})\times30\,cm/min $
$=8\pi r\times 30\,cm/min $
Thus, when $ r=40\,cm $,
$\frac{dS}{dt}=8\pi(40\,cm)\times30\,cm/min $
$=9600\pi\,cm^{2}/min $
