A stone is dropped into a quiet lake and waves move in circles speading out radially at the speed of `5` `cm//s`. At the instant when the radius of the circular wave is `8 cm`, how fast is the enclosed area increasing?

Options

A. `80 pi cm^(2)//s`
B. `90 pi cm^(2)//s`
C. `85 pi cm^(2)//s`
D. `89 pi cm^(2)//s`

Answer

A

Explanation

Enclosed area: `A= pi r^(2)`
so `(dA)/(dt)=2pi r(dr)/(dt)`
Here `r=8 cm, (dr)/(dt)=5 cm//s`
`rArr (dA)/(dt)=(2pi) (8)(5)=80 pi cm^(2)//s`