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# Rate of Change of Height of Cone

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Gravel is dumped from a conveyor belt at the rate of 30 cubic feet per minute and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and heght are always equal. How fast is the height of the pile increasing when the pile is 10 feet high? include the correct units in your answer. Let h=the height of the pile. The volume, V, of a cone of radius r and height h is given by V=(1/3) pi r^2 h.
dh/dt = ___________

https://brainmass.com/math/calculus-and-analysis/rate-of-change-of-height-of-cone-31844

#### Solution Preview

V=(1/3) pi*r^2*h

But r = h

Therefore,

V = (1/3)*pi*h^2*h = ...

#### Solution Summary

The Rate of Change of the Height of a Cone is calculated. The solution is detailed and well presented.

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