Math CentralQuandaries & Queries


Question from Susan, a student:

I have this problem on a homework assignment and just can't seem to figure it out:
A circular oil slick of uniform thickness is caused by a spill of 1 m^3 of oil. The thickness of the oil is decreasing at the rate of .001m/h. At what rate is the radius of the slick increasing when the radius is 8.
This is what I have set up:
1 = pi*r^2*h
dV/dt = 2*pi*r*dr/dt*dh/dt
= 2*pi*8*dr/dt*- 0.001

But i still have the dV/dt to deal with, and I don't know what to do with it.

Hi Susan,

There is a fixed volume of oil, 1 cubic metre, so V = 1 cu metre and dV/dt = 0 m3/h.

You have however differentiated π r2 h incorrectly. π is a constant and r2 h is a product so you need to use the product rule. Try to complete the problem now and write back if you need more assistance.


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