A conical salt spreader is spreading salt at a rate of 1 cubic feet per minute. The diameter of the base of the cone is 4 feet and the height of the cone is 5 feet. How fast is the height of the salt in the spreader decreasing when the height of the salt in the spreader (measured from the vertex of the cone upward) is 3 feet? Give your answer in feet per minute.

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anonymous · Answer

Okay so you know that [v=pi/3(r ^{2})(h)\]. So in order to differentiate the problem you need to get rid of your r, since you don't know the value of dr/dt. To do this, you can use the ratio of radius to height, since in a cone that is consistent. when r=2, h=5, therefore (2/5)h=r. You can plug this value in for r in your volume of a cone formula, and then you should be able to find the derivative and solve for dh/dt.