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Rate of Change - Just checking

  1. Dec 3, 2007 #1
    [SOLVED] Rate of Change - Just checking

    1. The problem statement, all variables and given/known data

    Sand is poured into a conical pile with the height of the pile equaling the diameter of the pile. If the sand is poured at a constant rate of 5m^3/s at what rate is the height of the pile increasing when height is 2 meters.

    2. Relevant equations

    v = [tex](1/3)\pi r^2[/tex]
    r' = h' / 2 (i think this is right - not sure)

    3. The attempt at a solution

    So i got
    v' = [tex](1/3)\pi (2rr'h + r^2h')[/tex]

    So i have 2 unknowns r' and h'. Since we can make the connection that r' = h'/2 i replace that in the equation and get:

    v' = [tex](1/3)\pi (2r(h'/2)h + r^2h')[/tex] ->

    r = 1
    h = 2


    v' = [tex](1/3)\pi (2h' + h')[/tex] ->
    h' = [tex]5/\pi[/tex]

    Im not sure if this answer is right but if you can please check over my work, i would appreciate it.

  2. jcsd
  3. Dec 3, 2007 #2


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    Staff Emeritus
    Science Advisor

    It would have been better to have clearly stated somewhere that v'= 5, but it's obvious that you did use that. Yes, that is the correct answer.
  4. Dec 3, 2007 #3
    Sorry i thought it was in the problem question i posted.

    Well thanks!
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