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?

Explanation

Let r be the radius and A be the area of the wave.
Given `(dr)/(dt) = 5 cm//sec`
Now, `A= pi r^(2)`
`rArr (dA)/(dt) = 2 pi r (dr)/(dt)`
at r = 8
` (dA)/(dt)= 2pi xx 8xx5 = 80 pi cm^(2)//sec`