Answer
$\displaystyle \frac{dA}{dt}=8\pi r\cdot\frac{dr}{dt}$
Work Step by Step
$r=r(t)$ so, by the chain rule,
$\displaystyle \frac{dA}{dt}=\frac{dA}{dr}\frac{dr}{dt}$
$\displaystyle \frac{ds}{dr}=\frac{d}{dr}[4\pi\cdot r^{2}]=4\pi\cdot 2r=8\pi r$
$\displaystyle \frac{dA}{dt}=8\pi r\cdot\frac{dr}{dt}$
