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March 1, 2015

Posted by **kim** on Thursday, October 14, 2010 at 12:26pm.

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 -
**drwls**, Thursday, October 14, 2010 at 1:18pmdV/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 -
**kim**, Thursday, October 14, 2010 at 11:56pmThank you very much

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