Chapter 3, Problem 50RE

Volume of an Oil Spill An offshore oil well is leaking oil onto the ocean surface, forming a circular oil slick about $0.005$ meter thick. If the radius of the slick is $r$ meters, the volume of oil spilled is $V=0.005\pi r^2$ cubic meters. If the oil is leaking at a constant rate of $20$ cubic meters per hour so that $\frac{dV}{dt}=20$, find the rate at which the radius of the oil slick is increasing at a time when the radius is $50$ meters. $\left[\text{Hint:}\text{ Find a relation between }\frac{dV}{dt}\text{and}\frac{dr}{dt}\right]$