Question

The radius of circular plate is 2 cm. If it is being heated the expansion in its radius happens at the rate of 0.02 cm/sec. Find the rate of expansion of the area when the radius is 2.1 cm.

Answer 1

We have,

Radius $r=2.cm.$

$Rate=\frac{dr}{dt}=0.02cm/\sec .$

We know that,

Area of circle $=\pi r^2$

On differentiating and we get,

$\frac{dA}{dt}=2\pi r\frac{dr}{dt}$

$\frac{dA}{dt}=2\pi \times 2.1\times 0.02$

$\frac{dA}{dt}=0.084\pi c.m{.}^2/sec.$

Hence, the rate of expansion of the area is $0.084\pi c{m}^2/sec$

This is the answer.