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Math Help - Related Rates problem

  1. #1
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    Related Rates problem

    I don't understand this problem at all. Can someone please help me break it down? I would post my work if I even knew how to start it but I don't.

    Sand falls from a conveyor belt onto the top of a conical pile at a constant rate of 15 m^3/min. The height of the pile is always 3/5 of the base diameter. How fast is the height changing when the pile is 3 m high? At the same instant, how fast is the base radius changing?
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  2. #2
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    V = \frac{\pi}{3} r^2 h

    h = \frac{3}{5}d = \frac{3}{5}(2r) = \frac{6}{5}r

    sub the last expression for h to get the volume formula strictly in terms of the variable r.

    take the time derivative.

    solve for \frac{dr}{dt}.

    take the time derivative of h = \frac{6}{5}r and calculate \frac{dh}{dt}.
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