Question

A circular disc of radius $3cm$ is being heated. Due to expansion, its radius increases at the rate of $0.05cm/s$. Find the rate at which its area is increasing when the radius is $3.2cm$.

Answer 1

Initially Radius, $r$ of the circular disc is $3$ cm.

Radius is increasing at the rate of $0.05$ cm/s

So,

$\frac{d\left(r\right(t\left)\right)}{dt}=0.05$

Area at time $t$,

$A\left(t\right)=\pi {\left[r\right(t\left)\right]}^2$

Rate of change of area,

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

When radius is $3.2$ cm , area is increasing at the rate of,

$=2\pi \left(3.2\right)\left(0.05\right)$

$=0.32\pi$ $c{m}^2/s$