# calculus

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At a sand & gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 16 cubic feet per minute. The diameter of the base of the cone is approximately three times the altitude. At what rate is the height of the pile changing when the pile is 12 feet high?

• calculus -

dV/dt = 16 ft^3/min

V = (1/3)*pi*R^2*H
= (1/12)*pi*D^2*H = (1/12)*pi^(3H)^2*H
= (3/4)*pi*H^3

dV/dt = (9/4)*pi*H^2*dH/dt = 16

Solve for dH/dt when H = 12

• calculus -

Thank you very much

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