Answer
a.) $\frac{dA}{dt}$ = $2\pi r\frac{dr}{dy}$
b.) $\frac{dA}{dt}$ $\approx$ 188.50 m/s
Work Step by Step
Given: radius(r) = 30 m; $\frac{dr}{dt}$ = 1 m/s
a.) $A_{circle}$ = $\pi r^{2}$
$\frac{d}{dt}(A)$ = $\frac{d}{dt}(\pi r^2)$
$\frac{dA}{dt}$ = $2\pi r\frac{dr}{dt}$
b.) Substitute:
$\frac{dA}{dt}$ = $2\pi(30)(1)$
=$2\pi(30)$
=$6.28318530718(30)$
$\approx$ $188.50$ $m^2/s$
