## Thomas' Calculus 13th Edition

$\dfrac{dS}{dt} = 8\pi r \dfrac{dr}{dt}$
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, $\dfrac{dS}{dt} = 8\pi r \dfrac{dr}{dt}$