Question

The radius of a circular plate is increasing at the ratio of $0.20$ cm/sec.At what rate is the area increasing when the radius of the plate is $25$ cm.

Answer 1

Given the radius of the circular plate is $=r=25$ cm.

Again rate of increase of radius $=\frac{dr}{dt}=0.20$ cm/sec.

The area of the circular plate $=A=\pi r^2$ cm${}^2$.

Now rate of increase in area of the plate is $\frac{dA}{dt}=2\pi r\frac{dr}{dt}=50\times 0.20\pi =10\pi$ cm${}^2$/sec.