Answer
$180 \pi $ $ft^2/s$
Work Step by Step
Let
Area =A
Radius=r
Then
$A=\pi r^2$
Taking derivative with respect to t
$\frac{dA}{dt}=\frac{d(\pi r^2)}{dt}=\frac{d(\pi r^2)}{dr} \frac{dr}{dt}=\pi \frac{d(r^2)}{dr} \frac{dr}{dt}=2\pi r \frac{dr}{dt}$ ................ eq(1)
Now according to the given condition
$r=\frac{dr}{dt}\times t$ .................... eq (2)
Put $t=10$sec, $\frac{dr}{dt}=3 $ft/sec in equation (2) $\Longrightarrow$
$r=3\times10=30 ft$
Putting $r=30 $ft, $\frac{dr}{dt}=3 $ft/sec in equation (1)
$\frac{dA}{dt}=2\pi \times 30 \times 3=180 \pi$ $ft^2/s$
