## Calculus (3rd Edition)

a) $100\pi \,m^{2}/min$ b) $24\pi\, m^{2}/min$
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, $\frac{dA}{dt}=2\pi(6\,m)\times2\,m/min$ $=24\pi\, m^{2}/min$