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Calculus Rate Problem HELP!?

The top of a silo has the shape of a hemisphere of diameter 20 feet. If it is coasted uniformly with a layer of ice, and if the thickness of the ice is decreasing at the rate of .25 in/hr, how fast is the volume of the ice changing when the ice is 2 in. thick?my teacher says there will be a problem like this on the test so please explain.


The radius of the hemisphere is 120 inches. The radius of the top layer of ice is 122 inches. Volume = 4pi(r)^3 / 3 => dV/dt = 4pi(r)^2 dr/dt = 4 pi (122)^2 (-.25) = -46759.47 inch^3 / hour.

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