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Rate of oil circle... calculus problem?
A ruptured oil tanker causes a circular oil slick on the surface of the ocean. When its radius is 150 meters, the radius of the slick is expanding by 0.1 meter/minute and its thickness is 0.02 meter. At that moment:
a) how fast is the area of the slick expanding?
I got 94 meter^2/minute
b) The circular slick has the same thickness everywhere and the volume of oil spilled remains fixed. How fast is the thickness of the slick decreasing?
How do I do part b in this question?
1 Answer
- 1 decade agoFavorite Answer
The oil slick is being modeled as a cylinder:
V = Pi(R^2)T where
V is the volume of the slick (constant!)
R is the radius of the slick
T is the thickness
Taking the derivative of both sides with respect to time:
0 = Pi(R^2)(dT/dt) + Pi(T)[2R(dR/dt)
Solve for the unknown, dT/dt
The trick is remembering that dV/dt = 0 because the volume is constant.