Answer
$\frac{dS}{dt} = 8\pi r \frac{dr}{dt}$
Work Step by Step
Surface area of a sphere (S) is determine by the equation $4\pi r^2$
so S = $4\pi r^2$
on differentiation of the surface area with respect to time, we get:
$\frac{dS}{dt}$ = $\frac{d4\pi r^2}{dt}$
we obtain: $\frac{dS}{dt} = 8\pi r \frac{dr}{dt}$
the final answer: is $\frac{dS}{dt} = 8\pi r \frac{dr}{dt}$
