Question

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

Answer 1

Let $r$ be the radius

Given, Radius of a circle is increasing at the rate of $0.7\text{cm/s}$, so

$\frac{dr}{dt}=0.7\text{cm/s}$

Circumference of circle $C=2\pi r$

Now,

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

$\Rightarrow \frac{dC}{dt}=2\pi \frac{dr}{dt}$

$\Rightarrow \frac{dC}{dt}=1.4\pi \text{cm/s}$

$[\because \frac{dr}{dt}=0.7]$

Hence, circumference of circle is increasing at the rate of $1.4\pi \text{cm/s}$.