Answer
$\dfrac{dA}{dt}=\pi\dfrac{cm^2}{min}$
Work Step by Step
Given: $\frac{dr}{dt}=0.01\frac{cm}{min}$ AND radius, $r=50 cm$; Area, $A=\pi r^2$
Now, on differentiating both sides, we get:
$\dfrac{dA}{dt}=2\pi r \frac{dr}{dt}$
when $r=50cm$, thus:
This implies $\dfrac{dA}{dt}=2\pi (50)\times 0.01$
or, $\frac{dA}{dt}=\pi\frac{cm^2}{min}$
Hence, $\dfrac{dA}{dt}=\pi\dfrac{cm^2}{min}$
