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Weird Depth Problem

  1. Sep 23, 2007 #1
    I've looked everywhere to try to solve this problem and I can't find anything. It is:

    A conical tank (with vertex down) is 10 feet across the top and 12 feet deep. If water is flowing into the tank at a rateof 10 cubic feet per minute, find the rate of change of the depth of the water when the water is 8 feet deep.

    Thanks for the help.
  2. jcsd
  3. Sep 23, 2007 #2
    this is a pretty easy related rates problem
  4. Sep 23, 2007 #3


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    Why would you consider that weird? In general, if you can find a formula for volume as a function of height, V(h), then, by the chain rule, dV/dt= (dV/dh) dh/dt. You are given dV/dt and asked to find dh/dt. You need to be able to calculate dV/dh. Do you know (or can you look up) the formula for volume of a cone in terms of radius and height? Here you are told that the tank itself has height 12 feet and radius 5 feet. Do you see that any "cone of water" contained by that tank will have h/r= 12/5?
  5. Sep 24, 2007 #4
    sorry, i just started rates on friday
  6. Sep 24, 2007 #5


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    Good! Then you should know exactly how to do this!
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