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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 equal. How fast is the height of the pile increasing when the pile is 11 feet high?

Recall that the volume of a right circular cone with height h and radius of the base r is given by


  • Math -

    If you are in calculus...

    V=PI *r^2 * r/3 because r and h are the same
    V=PI *h^3 /3

    dV/dt=PI*h^2 dh/dt
    You know dv/dt as 20ft^3/min
    solve for dh/dt.

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