(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Water is being drained from a container which has the shape of an inverted right circular cone. The container has a radius of 5.00 inches at the top and a height of 7.00 inches. At the instant when the water in the container is 4.00 inches deep, the surface level is falling at a rate of 0.7 in/sec. Find the rate at which water is being drained from the container.

2. Relevant equations

v=1/3 pi r^2 h

3. The attempt at a solution

The values I came up with are as follows.

h=4 (of water level)

r=2.86 (of water level found using equal triangles)

dV/dt= what I am solving for

dh/dt = -0.7

Whenever I take the derivative of the volume equation I end up with a dr/dt that I have no idea what to do with. Am I just doing it wrong and getting the dr/dt when I shouldn't?

I also noticed in a few google results they'd used similar triangles to get r in terms of h. But whenever I do that, I get an actual value for r and the h goes away. Perhaps this is where I am messing up?

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# Related Rates Involving a Cone

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