The area A = πr2 of a circular oil spill changes with the radius. At what rate does the area change with respect to the radius when r = 7 ft?

Question

The area A = πr² of a circular oil spill changes with the radius. At what rate does the area change with respect to the radius when r = 7 ft?

MULTIPLE CHOICE

7π ft²/ft

49π ft²/ft

14π ft²/ft

14 ft²/ft

Answer 1

Given the area of a circle is πr² and this is a related rate problem, we wish to determine the rate of change of the area with respect to the radius.

A = πr² ft²

dA/dr = 2πr * dr/dr = 2πr ft²/ft

dA/dr = 2π * 7ft = 14π ft²/ft

The last answer