Calculus: Rates and Related Rates?

Question

A ruptured oil tanker causes a a circular oil slick on the surface of the ocean. When its radius is 150 meters, the radius on the slick is expanding by 0.1 meter/minute and its thickness is 0.02 meter. At that moment:

The circular slick has the same thickness everywhere, and the volume of the oil spilled remains fixed. How fast is the thickness of the slick decreasing?


Please Help

Answer 1

V = πr^2h
V/π = r^2h
Take the derivative of both sides:
0 = r^2dh + h(2rdr)
r^2dh = -2rhdr
dh = (-2h/r)dr
dh/dt = (-2h/r)dr/dt
dh/dt = [(-2(0.02))/150](0.1) = -0.000026666m/min
Thickness is decreasing at 2.6666 x 10^(-5)m/min