The radius of a circle is increasing uniformly at the rate of 3 cm/s. Find the rate at which the area of the circle is increasing when the radius is 10 cm.

Explanation

Here is the solution :

Let r be the radius of the circle.
Rate of increase = 3 cm/sec
`(dr) / dt = 3`

`A = pir^2`
`(dA) / dt = (d [pir^2]) / dt = 2pir ((dr) / dt)`
=` 2pir * 3`
= `6pir`
When the value of r = `10`, Rate of increase in area = `6pi * 10 = 60pi cm^2 per sec`