related rates calculus 1

gravel is being dumped from a conveyor belt at a rate of 15 ft^3/hr and its coarseness is such that it forms a pile in the shape of an inverted right cone whose height is three times its base radius. How fast is the height of the pile increasing when the pile has a height of 10ft

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  1. height ------- h
    base radius --- h/3

    V = (1/3)π r^2 h
    = (1/3)π (h^2/9)(h) = (π/27) h^3

    dV/dt = (π/9) h^2 dh/dt
    for the given data:
    15 = π/9 (100)dh/dt
    dh/dt = 135/(100π) ft/hr

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  2. How did you get "dh/dt = 135/(100π) ft/hr?"

    That's the only part I'm confused about.

    Thanks for your help btw.

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  3. from
    15 = π/9 (100)dh/dt

    I multiplied both sides by 9/(100π)
    which left me with dh/dt on the one side
    and 15(9/(100π) ) or 135/(100π) on the other side

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  4. oh okay, I ended up getting .43ft/hr. I'm 99% sure that's the correct answer.

    Thanks for clearing that up for me, I'm really ing at related rates, so I'm doing all the problems I can.

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