Question

The radius of a circle is increasing at the rate of $0.7cm/sec$. What is the rate of increase of its circumference ?

Answer 1

Circumference, $C=2\pi r$

$\frac{dC}{dt}=\frac{dC}{dr}\times \frac{dr}{dt}$

$=\frac{d}{dr}\left(2\pi r\right)\frac{dr}{dt}$

$=2\pi \frac{dr}{dt}=2\pi \left(0.7\right)=1.4\pi cm/sec$