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?

We know that area of a circle (A) is A = πr²

Then, Rate of change of the area with respect to time (t) is given by,

……………….. by chain rule

It is given that

Then,

Thus, when r = 8cm

Then

Therefore, when the radius of the circular wave is 8 cm, how fast is the enclosed area increasing is 80π cm²/s.