Question

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

Answer 1

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