# calculus

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Gravel is being dumped from a conveyor belt at a rate of cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always equal to each other. How fast is the height of the pile increasing when the pile is feet high?
Hint: The volume of a right circular cone with height and radius of the base is given by .

• calculus -

Diameter is equal to height, or
2r = h ---> r = h/2

V= (1/3)πr^2 h
= (1/3)π(h^2/4)(h)
= (1/12πh^3
dV/dt = (1/4)π h^2 dh/dt

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