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.

Options

A. `6 pi cm^(2)//s`
B. `10 pi cm^(2)//s`
C. `30 pi cm^(2)//s`
D. `60 pi cm^(2)//s`

Answer

D

Explanation

Given `(dr)/(dt)=3`
Let A= Area of circle `=pi r^(2)`
`therefore` (dA)/(dt)=2pi r (dr)/(dt)=6pj r`
Now `(dA)/(dt)|_(r=10)=6xx10xxpi=60 pi cm^(2)//s`