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Homework Help: Volume of three shared cylinders

  1. Aug 13, 2010 #1
    1. The problem statement, all variables and given/known data

    Calculate the volume of the space enclosed by three cylinders x2+y2=1, x2+z2=1, and y2+z2=1.

    2. Relevant equations

    Triple Integral.

    3. The attempt at a solution

    change to polar coordinates
    1. The problem statement, all variables and given/known data



    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Aug 13, 2010 #2

    Dick

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    If x^2+z^2=1 and y^2+z^2=1 then x^2=y^2=1-z^2. The cross sections of your surface are squares integrating dz. I definitely wouldn't change to polar coordinates.
     
  4. Aug 14, 2010 #3
    What is the range of z if I integrate w.r.t z?
     
  5. Aug 14, 2010 #4

    Dick

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    What's the range of z on the curve x^2+z^2=1?
     
  6. Aug 16, 2010 #5
    is it (+/-) sqrt of 1-x^2?
     
  7. Aug 18, 2010 #6

    Dick

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    Those are the values for single value of x. Suppose you consider all possible x?
     
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