a circle is expanding and growing at a constant rate of 3 inches per minute. How fast is the area of the circle changing at instant that the radius of the circle is 12 inches?

Question

1.     Supposes a circle is expanding in such a way that its radius is growing at a constant rate of 3 inches per minute. How fast is the area of the circle changing at instant that the radius of the circle is 12 inches?

Answer 1

The area of a circle is:

A = π·r²

Rate of change of the area is:

dA/dt = dA/dr · dr/dt

dA/dt = 2·π·r · dr/dt

r is given as 12 inches and dr/dt is given as 3 in/min. Plug in the numbers and compute the answer. The units are cm²/minute.