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Calculus (can someone please verify this?)

Gravel is being dumped from a conveyor belt at a rate of 30 ft^3/min. It forms a pile in the shape of a right circular cone whose base diameter and height are always the same. How fast is the height of the pile increasing when the pile is 19 feet high?

Vol = (1/3)pi (h^2/4)(h)
= (1/12)pi h^3

d(Vol)/dt = (1/4)pi h^2 dh/dt
30 = (1/12)pi(19^2) dh/dt
dh/dt=30*12/(pi*19^2)
dh/dt=0.317
My homework is online, and it says this is wrong... I tryed typing the whole equation and it still says it's wrong... can someone please check this and tell me what's wrong?

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Cecille

  1. "30 = (1/12)pi(19^2) dh/dt "
    Shouldn't it be
    30 = (1/4)πh^2 dh/dt?

    dV/dt = dV/dh * dh/dt
    dh/dt = dV/dt / dV/dh
    =30 / (πh^2/4)

    I get 0.1058 ft/min.
    Check the unit for the answer, as well as the format (decimals? how many? exact expressions?) the online homework systems usually instruct you the format expected.

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    MathMate

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