Question

The diameter of a circle increasing at the rate of $1$ cm. /sec. When its radius is $\pi$, the rate of increase of its area is $(\pi {)}^m$.Find $m$

Answer 1

$A=\frac{\pi d^2}{4}\frac{dA}{dt}=\frac{2\pi d}{4}\times \frac{dA}{dt}=\frac{2\pi }{4}\times 2\pi \times 1={\pi }^2,m=2$