The radius of a circle is increasing at a rate `((dr)/(dt))=alpha` . Find the rate at which its area is increasing when radius is equal to 3 m.

Explanation

area of cricle (A)`=pir^(2)`
`(dA)/(dt)=pi(2r)(dr)/(dt)=2pir((dr)/(dt))=2pir(alpha)`
`((dA)/(dt))_(atr=3m)=6pi alpham^(2)//sec`.