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

Let r be the radius and A be the area of the circle.
Given `(dr)/(dt) = 3 cm//sec`
Now ` A = pi r^(2)`
`rArr (dA)/(dt) = 2 pi r (dr)/(dt) `
at r = 10 cm
` (dA)/(dt) = 2 pi xx 10 xx 3 = 60pi cm^(2)//sec`