Answer
$\frac{dA}{dt}=\pi\frac{cm^2}{min}$
Work Step by Step
Given $\frac{dr}{dt}=0.01\frac{cm}{min}$
and radius (r)=50 cm
area (A)= $\pi r^2$
on differentiating both sides, we get:
$\frac{dA}{dt}=2\pi r \frac{dr}{dt}$
r=50cm, so:
$\frac{dA}{dt}=2\pi (50)\times 0.01$
$\frac{dA}{dt}=\pi\frac{cm^2}{min}$
Thus the final answer is:$\frac{dA}{dt}=\pi\frac{cm^2}{min}$
