Calculus - Related Rates

Question

The rate of change of the area of a circle is 260 in²/sec. How fast is the radius of a circle changing at the instant when its radius is 13 inches. Give units in your answer.

Answer 1

Area of a circle = pi times the radius squared

A = pi(r^2)

take the derivative with respect to time

A' = 2pir(r')

260 = 2pi(13)r'

260= 26pi(r')

r' = 10/pi inches per second = rate of change of the radius when r=13 inches