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Math Help - Inverted Cone related rate problem HELP!

  1. #1
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    Inverted Cone related rate problem HELP!

    Here the the problem that I can't crack on my final:

    A coffee filter has the shape of an inverted cone. Water drains out of the filter at a rate of 10 cc/min. When the depth of the water in the cone is 8 cm the depth is decreasing at 2 cm/min. What is the ratio of the height of the cone to its radius?

    Thanks in advance!
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  2. #2
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    The volume of a cone is given by V= \frac{1}{3}\pi r^2 h. If the "ratio of height to radius" is k, then h/r= k so that h= kr or r= h/k. Put that into the formula for volume to get V= \frac{1}{3}\pi (h/k)^2h= \frac{1}{3}\pi h^2/k^2[/itex]<br /> <br />
  Differentiate that with respect to t to find [itex]\frac{dV}{dt}= f(h,k)\frac{dh}{dt}. Now, you are given that dV/dt= -10 cc/min, dh/dt= -2 cc/min and h= 8 cm. Solve for k.
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