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March 27, 2017

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Gravel is being dumped from a conveyor belt at a rate of 10 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 18 feet high? (Recall that the volume of a right circular cone with height h and radius of the base r is given by
V = (1/3) * pi * r^2 * h)

  • Calculus - ,

    so, you know V, and

    dV/dt = 1/3 pi (2r dr/dt + dh/dt)

    You know h = 2r and that h = 18 and that dV/dt = 10.

    Piece o' cake, no?

  • Calculus - ,

    Ok, but i'm still a little confused on how I get dh/dt by itself

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