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Math Help - related rates

  1. #1
    Newbie
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    Oct 2007
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    related rates

    Gravel is being dumped from a conveyor belt at a rate of 20 cubic feet per minute. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing when the pile is 22 feet high?
    h=22
    r=11

    r=1/2h
    V=1/12*pi*h^3
    dv/dt=1/12*pi*h^2*dh/dt
    dv/dt=1/12*22^2*pi*dh/dt
    dv/dt=40.33pi*dh/dt
    where do i go from here?
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  2. #2
    MHF Contributor
    Joined
    Apr 2005
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    You are given, "Gravel is being dumped from a conveyor belt at a rate of 20 cubic feet per minute. "

    That is the rate of change of the volume of the pile. That is your dV/dt. Substitute 20 cuft/min for your dV/dt to get your dh/dt.
    So, one or two more steps in your computaion and you are done.
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