Related Rates: Fill in the Blank

Question

A circle is inside a square.

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

When the radius is 2 meters, and the sides are 20 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 hour.

Answer 1

Ler r = radius of the circle at time t and x = length of a side of the square at time t and A = area inside the square and outside the circle at time t.

Given: dr/dt = -5, dx/dt = 5

Find dA/dt when r = 2 and x = 20.

A = x² - πr²

dA/dt = 2x(dx/dt) - 2πr(dr/dt) = 40(5) - 4π(-5) = (200 + 20π) m²/hr