Calculus

Gravel is being dumped from a conveyor belt at a rate of 25 ft3/min, and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 6 ft high? (Round your answer to two decimal places.)

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  1. since h = 2r, r = h/2
    v = pi/3 r^2h = pi/12 h^3
    So,
    dv/dt = pi/4 h^2 dh/dt

    When h=6, we have

    25 = 9pi dh/dt

    Now just do the math

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  2. derp

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