Question

The radius of a circle is increasing uniformly at the rate of 5cm/sec. Find the rate at which the area of the circle is increasing when the radius is 6 cm.

Answer 1

Let radius of the circle be $r$

It is given that $\frac{dr}{dt}=5$ cm/sec

Now area of circle is given by, $A=\pi r^2$

$\Rightarrow \frac{dA}{dt}=2\pi r\frac{dr}{dt}$, differentiate both sides w.r.t. $t$

$\therefore \frac{dA}{dt}{|}_{r=6}=2\pi \left(6\right)\left(5\right)=60\pi$ cm/sec${}^2$