A stone is dropped into a quiet lake and waves move in circles 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. `40 pi cm^(2)//s`

Answer

A

Explanation

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