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Math Help - rate problem

  1. #1
    Junior Member
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    rate problem

    Water is withdrawn from a conical reservoir, 8 feet in diameter and 10 feet deep(vertex down) at the constant rate of 5 ft^3/min. How fast is the water level falling with the depth of the water in the reservoir is 5ft?

    Ok so I think when you use the volume formula, you replace 5 for the final height and im not sure what else to do, or if that is even right. Please help!!
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  2. #2
    Junior Member autumn's Avatar
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    unfortunalty, im stuck in hicks state. IN.
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    It looks like you're given that dV/dt=5 at that moment.
    You use similiar triangles where r=radius and h=height.

    So 4/10=r/h or r=.4h.

    Use V=\pi r^2h/3

    replace r and differentiate wrt t and plug away.

    V=\pi (.4h)^2h/3
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