Question

The radius of a circular oil slick on the surface of a pond is increasing at the rate of 10 meters/min. At what rate is the circle's area changing when the radius of the oil slick is 20 m. ?

Answer 1

$10\ m/min=0.167\ m/s$

$\Delta A=A_0-A=\pi R_0^2-\pi(R_0+0.167\cdot1)^2=3.14\cdot20^2-3.14\cdot(20+0.167\cdot1)^2=$

$=21\ (m^2/s)$. Answer