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Related Rates Coffee Filter Problem

  1. Nov 19, 2006 #1
    Coffee drains from a conical filter, with diameter of 15cm and a height of 15 cm into a cylindrical coffee pot, with a diameter of 15 cm at 2 cm^2/ sec. At a certain time, the coffee in the filter is 13 cm deep.

    a) How fast is the depth of coffee in the filter changing at that time?
    b) How fast is the depth of coffee in the pot changing at that time?

    Apparently this is an assignment question. I think that 2cm^2 / sec is a typo and should be replaced by 2cm^3 / sec.

    http://img242.imageshack.us/img242/3917/attemptau7.jpg [Broken]

    << that is my attempt for problem a), is this right? Can someone make any suggestions.. thanks in advance
    Last edited by a moderator: May 2, 2017
  2. jcsd
  3. Nov 20, 2006 #2
    I'm getting 8/(169 * Pi) cm/s as my answer. I think one place where you did something wrong was you did not square h/2 in place of r in the original volume equation. It should have looked something like this.

    v = 1/3 * PI * r^2 * h --> r = h/2 --> v = 1/3*Pi*(h/2)^2*h which gives

    v = 1/12*Pi*h^3 By differentiation we obtain:

    dv = 1/4*Pi*h^2*dh solving for dh we get (4*dv)/(Pi*h^2) or 8/(169*Pi) cm/s.
  4. Nov 20, 2006 #3
    thanks i got a, but can someone tell me for b i dont get it
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