Answer
$\dfrac{dS}{dt} = 8\pi r \dfrac{dr}{dt}$
Work Step by Step
Surface area of a sphere (S) can be found as: S = $4\pi r^2$
On differentiation , we get:
$\dfrac{dS}{dt}$ = $\dfrac{d (4\pi r^2)}{dt}$
or, $\dfrac{dS}{dt} = 8\pi r \dfrac{dr}{dt}$
Hence, $\dfrac{dS}{dt} = 8\pi r \dfrac{dr}{dt}$
