Answer
(b)$A=\pi r^2$
(c)$\frac{dA}{dt}=2 \pi r\frac{dr}{dt}$
(d) $\frac{dA}{dt}=20 \pi \frac{cm^2} {dt}$
Work Step by Step
(b) $A=\pi r^2$
(c)$ \frac{dA}{dr}=\frac{dA}{dt} \frac{dt}{dr}$
Putting $A=\pi r^2 $ in the RHS
$ \frac {d (\pi r^2)} {dr}= \frac{dA}{dt} \frac{dt}{dr} $
$ \pi \frac {d (r^2)} {dr}= \frac{dA}{dt} \frac{dt}{dr} $
$ \pi (2r) = \frac{dA}{dt} \frac{dt}{dr} $
$ \frac{dA}{dt} \frac{dt}{dr} =2\pi r$
$\frac{dA}{dt}=\frac {2 \pi r} {\frac{dt}{dr}} =2\pi r \frac{dr}{dt}$
$\frac{dA}{dt}=2\pi r \frac{dr}{dt}$ ................ eq (1)
(d) Putting $ r=5cm$ and $ \frac{dr}{dt}= 2 cm/s$ in equation (1)
$\frac{dA}{dt}=2\pi \times 5\times 2=20 \pi \frac{cm^2} {s}$
