Given: a stone is dropped into a quiet lake and waves move in circles at a speed of 4 cm/sec.

To find the instant when the radius of the circular wave is 10 cm, how fast is the enclosed area increasing

Let r be the radius of the circle and A be the area of the circle

When stone is dropped into the lake waves moves in circle at speed of 4cm/sec.

i.e., radius of the circle increases at a rate of 4cm/sec

i.e.,

We know that

Area of the circle is

Now,

So when the radius of the circular wave is 10 cm, the above equation becomes,

Hence the enclosed area is increasing at the rate of 80 cm²/sec