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Math Help - Rate of change

  1. #1
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    Rate of change

    Gravel is being dumped from a conveyor belt at a
    rate of 40 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
    18 ft high?
    The height is increasing at ?? ft/min?
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  2. #2
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    Quote Originally Posted by Johnson View Post
    Gravel is being dumped from a conveyor belt at a
    rate of 40 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
    18 ft high?
    The height is increasing at ?? ft/min?
    you are given ...

    \frac{dV}{dt} = 40 \, ft^3/min

    2r = h

    gravel pile is in the form of a cone ... V = \frac{\pi}{3} r^2 h

    the problem wants you to find \frac{dh}{dt} when h = 18 \, ft

    get the volume in terms of h , take the derivative w/r to time, and substitute your given values. finally, solve for \frac{dh}{dt}.
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