Answer
a) $100\pi \,m^{2}/min $
b) $24\pi\, m^{2}/min $
Work Step by Step
a) $\frac{dA}{dt}=\frac{dA}{dr}\times\frac{dr}{dt}=\frac{d}{dr}(\pi r^{2})\times2\,m/min $
$=2\pi r\times2\,m/min $
When $ r=25 \,m $, $\frac{dA}{dt}=2\pi(25\,m)\times2\,m/min $
$=100\pi \,m^{2}/min $
b) As $\frac{dr}{dt}=2\,m/min $ and r(0)=0, after 3 minutes, the radius will be equal to $3\,min\times2\,m/min=6\,m $
Then, $\frac{dA}{dt}=2\pi(6\,m)\times2\,m/min $
$=24\pi\, m^{2}/min $
