The rate of change of surface area of a sphere of radius $r$ when the radius is increasing at the rate of $2 cm/ sec$ is proportional to

Let $S$be the surface area and $r$be the radius of the

sphere at any time$t$. Then, 

$\begin{array}{l} S=4\pi r^2\\ \Rightarrow \frac{dS}{dt}=8\pi r\frac{dr}{dt}\\ \Rightarrow \frac{dS}{dt}=8\pi r\times 2 \left[\frac{dr}{dt}=2\mathrm{cm}/\sec \right]\end{array}$

$\Rightarrow \frac{dS}{dt}=16\pi r\Rightarrow \frac{dS}{dt}\propto r$