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Definite integral distance from volume

  1. Jul 26, 2008 #1
    1. The problem statement, all variables and given/known dataIf you have a water tower that is spherical with a radius 20m, how far from the bottom will the water level be if it is filled to 1/4 of it's capacity.



    2. Relevant equations[tex]\int_-20^20pi(400-y^2)dy=33510.32164m^3=3,351,032.164Liters[/tex]



    3. The attempt at a solution I can find 1/4 capacity=837,758.041 liters but don't know where to go from here to find the distance from the bottom
     
  2. jcsd
  3. Jul 26, 2008 #2
    I meant for it to be a definite integral from 20 to -20 not 20 squared
     
  4. Jul 26, 2008 #3

    Dick

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    Instead of integrating from -20 to 20 to get the full volume, integrate from -20 to h. You'll get a cubic expression in h. Equate that to 1/4 of the full volume and try to solve for h.
     
  5. Jul 26, 2008 #4

    Dick

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    BTW it looks like you have to use numerical techniques to get an answer. The cubic doesn't factor or anything for me.
     
  6. Jul 26, 2008 #5
    Thanks for the help, I can use newtons method to approximate f(y) at zero and solve it from there thanks I would have never thought to set it to y
     
  7. Jul 27, 2008 #6
    By the way, two of the roots are complex numbers from what I got.. just a warning.
     
  8. Jul 27, 2008 #7
    I figured it out its 13.054073m from the bottom you either solve for zero with newtons method or graph it
     
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