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Cylindrical coordinate limits

  1. May 3, 2009 #1
    Hi Guys,

    I have been given the coordinates of a cylinder inside a sphere and want to convert to Cylindrical coordinates to compute the volume of the cylinder.

    Can you please check the limits and integral I have?

    The cylinder is x^2+y^2= 4

    sphere = x^2+y^2+z^2= 9

    As its a cylinder we have

    Limits are 0<= theta <= 2\pi 0<= r <= 2 and

    Inside a sphere with limits

    sphere = x^2+y^2+z^2= 9

    z = sqrt{9-r^2}

    So would my integral be:


    \int{{0}{2\pi} \int{0}{2} \int{0}{sqrt{9-r^2}} r dz dr d(theta)


    regards
     
  2. jcsd
  3. May 3, 2009 #2

    arildno

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    Why should the lower limit of z be 0?

    Are you sure about z=sqrt(9-r^2)) is the only limit set upon z by the above equation?
     
  4. May 3, 2009 #3
    Sorry I want to compute the solid bounded above and below by the sphere and inside the cylinder.

    I see your point the sphere can be either side of the z axis .

    it should be:

    int{-sqrt{9-r^2}} {sqrt{9-r^2}} r d(theta)


    Is that alright
     
  5. May 4, 2009 #4

    arildno

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    That's right indeed. :smile:
     
  6. May 4, 2009 #5
    Thanks for your help!
     
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