## Calculus: Early Transcendentals 8th Edition

$S'(8) = 128\pi \frac{cm^{2}}{min}$
$S(r) = 4\pi r^{2}$ Use the chain rule: $\frac{dS}{dt} = \frac{d(4\pi r^{2})}{dr}$ $\frac{dS}{dt} = 8\pi r \times \frac{dr}{dt}$ $\frac{dr}{dt} = 2 \frac{cm}{min}$ $\frac{dS}{dt} = 8\pi (8) \times 2$ $\frac{dS}{dt} = 64\pi \times 2$ $\frac{dS}{dt} = 128\pi \frac{cm^{2}}{min}$