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Volume of the intersection of two cylinders by polar co-ordinates

  1. May 26, 2009 #1
    Volume of the intersection of two cylinders by cylinderical co-ordinates

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


    find Volume of the intersection of two cylinders by cylindrical co-ordinates


    3. The attempt at a solution

    IN the attached file I found it's 8(a^3)/3
    It should be 16 not 8
     

    Attached Files:

    Last edited: May 27, 2009
  2. jcsd
  3. May 27, 2009 #2
    I know that the mistake may be trivial but can anyone give me any comment!!!!!!!1
     
  4. May 27, 2009 #3

    Dick

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    Why do you think the upper limit of the dz integration is r*cos(theta)? Don't you have z=sqrt(a^2-y^2)=sqrt(a^2-r^2*sin(theta)^2)?
     
    Last edited: May 27, 2009
  5. May 27, 2009 #4
    But in the first octent
    x^2 + y^2 = r^2
    y^2 + z^2 = r^2

    so z=x=rcos(theta)

    Isn't it?
     
  6. May 27, 2009 #5

    Dick

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    That's only true along the curve where the two cylinders intersect. It's not true everywhere on the surface in the first octant.
     
  7. May 27, 2009 #6

    Thanks Thanks Thanks
     
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