calulus 1 mathematics

Question

A circle is inside a square.

The radius of the circle is decreasing at a rate of 4 meters per minute and the sides of the square are decreasing at a rate of 1 meter per minute.

When the radius is 2 meters, and the sides are 24 meters, then how fast is the AREA outside the circle but inside the square changing?

The rate of change of the area enclosed between the circle and the square is _  square meters per minute.

Answer 1

The area A you are interested is s² - πr²

and dA/dt = 2s (ds/dt) - 2πr (dr/dt).

Just plug in the values given and get your answer.