The rate of change of the area enclosed between the circle and the square is----- square meter per day

Question

A circle is inside a square.

The radius of the circle is increasing at a rate of 5 meters per day and the sides of the square are decreasing at a rate of 1 meter per day.

When the radius is 6 meters, and the sides are 21 meters, then how fast is the AREA outside the circle but inside the square changing?

Answer 1

A = s² - πr²

DA/dt = 2s(ds/dt) - 2πr(dr/dt)

Now plug in the numbers in the problem to get the answer.