The circumference of a circle is increasing at a rate of 2pi/5 inches per minute. When the radius is 5 inches, how fast is the area of the circle increasing in square inches per minute?

Question

A. 1/5
B. pi/5
C. 2
D. 2pi
E. 25pi

Answer 1

since dC/dt = 2π/5, dr/dt = 1/5
a = πr^2, so
da/dt = 2πr dr/dt = 2π(5)(1/5) = 2π