Pre-Calc

posted by Vanessa

a conveyor makes a conical pile of mulch which has a height that is 2/3 of the diameter
The conveyor can deliver 10 cubic yards of mulch to the pile per minute. What is the function for the height of the pile as a function of time

  1. Steve

    v = 1/3 π r^2 h
    Now, h = 2/3 d = 4/3 r, so r = 3/4 h
    v = 1/3 π (3/4 h)^2 h = 3π/16 h^3
    Since v increases at a constant 10 yd^3/min,
    v(t) = 10t = 3π/16 h^3
    h^3 = 160t/3π
    h(t) = 2∛(20t / 3π)

  2. scott

    v = h * π * (3/4 h)^2 = 9/16 * π * h^3

    v = 10 t

    h(t) = [160 t / (9 π)]^(1/3)

  3. scott

    forgot the 1/3 in the volume equation

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