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Nailing down related rates questions

  1. Jan 6, 2005 #1

    I am terrible when it comes to doing these questions. I was wondering if you guys have any tips on how to do these questions. Like for example, just say there's a question like the following:

    Water is poured into a reservoir in teh shape of a cone 6ft. tall with a radius of 4ft. If water level is rising at 0.5ft/s. How fast is the water being poured at the instant the depth is 2ft?

    When I see that kind of question, I am clueless on how to even start it out. Is there a trick to doing them? I just don't understand the concept literally.

    Any hlep would be great thanks.
  2. jcsd
  3. Jan 6, 2005 #2


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    [tex] V(r(t),h(t))=\frac{\pi r^{2}(t)h(t)}{3} [/tex]

    U're interested in the quantity
    [tex] \frac{dV(r(t),h(t))}{dt}|_{h=2ft} [/tex]

  4. Jan 6, 2005 #3


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    The trick is to first transcribe all the given data into equations and write them down. Then write down in the same form, what the question (the desired quantity) translates to.

    Do this for the given example and then you'll see how the given data can be related to the required quantity.
  5. Jan 6, 2005 #4


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    When practicing these sorts of problems, don't even bother trying to solve them, just practice translating the problems into a mathematical question.

    Why? It's too easy to get distracted by solving the problem, and forget to work on the part you need to practice!
  6. Jan 11, 2005 #5
    The first thing you have to do is find the relationship between r and h in this case (6/4)=(h/r) so r=((2h)/3), with this relationship of everypoint on the cone, you can plug back into your original formula for the volume of a cone, plugging if for r in terms of h, then simplify, take the derivative, and solve with the infomation given.
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