The radius r of a circle is increasing at a rate of 5 centimeters per minute. Find the rates of change of the area (in cm2/min) when r = 39 centimeters.

Answer 1

This is a related rates problem. Use the formula for the area of a circle: A = π r².

Differentiate both sides with respect to t:

A = π r²

dA/dt = π x 2r dr/dt

Since radius is increasing 5 cm/min, we can replace dr/dt with 5.

They are asking for dA/dt (the rate of change of the area) when r = 39. So we replace r with 39.

Solve for dA/dt.

So we have dA/dt = π x 2 x 39 x 5 = 390π cm²/min.