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Differential Calculus - Related Rates

  1. Nov 10, 2012 #1
    1. The problem statement, all variables and given/known data

    A liquid is being filtrated by a filter with a cone form. The filtring tax is 2cm^3/min. The cone has 16cm height, 4 cm radius. The volume V is given by pi*r^2*y/2 where y is the height, r the radius. Discover a formula that relates the tax of variation of the liquid height with the height (y I guess).

    2. Relevant equations

    dV/dt = V*dh/dt
    V=pi*r^2*y/3

    3. The attempt at a solution

    the volume is = pi*r^2*y/3

    so Volume = pi.(4^2)*y/3

    Volume=16*pi*y/3

    dv/dt = 16*pi/3*dh/dt

    -2 = 16*pi/3 dh/dt

    dh/dt = -6/16*pi

    But this solution is incorrect :/ Can anyone tell me where I missed?

    Thanks in advance
     
  2. jcsd
  3. Nov 10, 2012 #2

    tiny-tim

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    welcome to pf!

    hi ruiwp13! welcome to pf! :smile:

    (try using the X2 button just above the Reply box :wink:)
    nooo :redface: … r is a function of y, not fixed

    so the volume is a multiple of y3 :wink:
     
  4. Nov 10, 2012 #3
    Re: welcome to pf!

    didn't follow you there :/ what do you mean?
     
  5. Nov 10, 2012 #4

    tiny-tim

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    the volume is a function of the radius (of the liquid surface) at time t, and the height at time t

    the radius at time t is not 4, it depends the height :wink:
     
  6. Nov 10, 2012 #5
    The maximum height being 16 and the radius 4 we can assume the radius y/4 or square(y)? is that it?
     
  7. Nov 10, 2012 #6

    tiny-tim

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    yes, radius = y/4 :smile:
     
  8. Nov 10, 2012 #7
    So now I have volume = pi*y*((y/4)^2)/3

    volume = pi*y^3/48

    dV/dt = pi*y^2/48 dy/dt

    -2 = pi*y^2/48 dy/dt

    dy/dt = 96*y^2/pi

    still incorrect :/ I'm doing this exercise for a friend. I don't remember the subject that well. I'm doing something wrong or something missing probably. Sorry for the incovinience
     
  9. Nov 10, 2012 #8

    tiny-tim

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    nooo :wink:
     
  10. Nov 10, 2012 #9
    Is the formula that is incorrect? Because I don't have the formulas anymore... I'm helping a friend. I remembered it had something to do with related rates :p sorry to bother you

    Or is it dV/dt = pi*3*y^2/48 dy/dt

    Then -2 = pi*3*y^2/48 dy/dt

    dy/dt = -96/pi*3*y^2

    dy/dt = -32/pi*y^2 it's correct!

    Thanks, a lot! Really helped me!
     
    Last edited: Nov 10, 2012
  11. Nov 10, 2012 #10

    tiny-tim

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    Yup! :biggrin:

    (you knew that! :wink:)​
     
  12. Nov 10, 2012 #11
    Really, thank you! I appreciated that you didn't give me the answer and helped me get there "by myself". Really nice forum.
     
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