March 30, 2017

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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 to each other. How fast is the height of the pile increasing when the pile is 23 feet high?

  • Please help Math - ,

    volume of cone = (1/3)pi(r^2)h
    but h=2r
    or r = h/2
    then volume = (1/12)pi(h^3)
    dV/dt = (1/4)pi (h^2) dh/dt

    20 = (1/4)pi (23^2)dh/dt

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