Question

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?

Answer 1

The area of a circle (A) with radius (r) is given by A=πr²
Therefore, the rate of change of area (A) with respect to time (t) is given by,

Hence, when the radius of the circular wave is 8 cm, the enclosed area is increasing at the rate of 80π cm²/s.