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Homework Help: Related Rates

  1. Mar 8, 2009 #1
    Sand is falling into a cone whose height is always 1/2 the diameter of the base. If the sand is falling at a rate of 1/2 cubic meters per min. How fast is the height increasin when the pile is 3 meters high?

    so far i've drawn my diagram and got this far.

    h = 1/2 the base
    dv/dt = +1/2m3/min


    the equation i was going to use is
    V = 1/12pih3

    then i get

    dv/dt = (1/2pi)(3h2)dh/dt

    i dont know how to get the h?
    any help?
  2. jcsd
  3. Mar 8, 2009 #2


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    Homework Helper
    Gold Member

    You're asked to find dh/dt when the height is 3 meters....so h=3:wink:

    But there is a problem with your starting equation V = (1/12)pih3....If the height is always half the diameter, then r=4h not h/4
  4. Mar 8, 2009 #3
    ok, that was stupid of me,
    i dont even know why i was having trouble with that now >.<
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