Question

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

Answer 1

The circumference of a circle $\left(C\right)$ with radius $\left(r\right)$ is given by $C=2\pi r$.
Therefore, the rate of change of circumference $\left(C\right)$ with respect to time $\left(t\right)$ is given by,
$\frac{dC}{dt}=\frac{dC}{dr}\cdot \frac{dr}{dt}$ (By chain rule)
$=\frac{d}{dr}\left(2\pi r\right)\frac{dr}{dt}$
$=2\pi \cdot \frac{dr}{dt}$
It is given that $\frac{dr}{dt}=0.7cm/s$
Hence, the rate of increase of the circumference is $2\pi \left(0.7\right)=1.4\pi cm/s$.