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Homework Help: Volume of a Region inside a cylinder and sphere (Symbolic)

  1. Nov 15, 2016 #1
    1. The problem statement, all variables and given/known data
    Suppose W is the region inside the cylinder x^2+y^2=a^2 and inside the sphere x^2+y^2+z^2=b^2, where 0<a<b.
    Set up an iterated integral for the volume of W

    2. Relevant equations
    3. The attempt at a solution
    I converted to cylindrical coordinates and tried to set up the triple integral as follows
    [rdzdthetadr], where -sqrt(b^2-r^2)<=z<=sqrt(b^2-r^2), 0<=theta<=2pi, 0<=r<=a. Am I at least on the right track for the integral? Any help is seriously appreciated. Thank you! :)
    P.S. (<= is meant to be 'less than or equal to'), just figured I'd clarify :)
  2. jcsd
  3. Nov 15, 2016 #2


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    That looks correct.
  4. Nov 16, 2016 #3
    Thank you for the reply. I spend way longer than I should have on this problem. I thought it was more complicated than this, so I am happy that the solution was easier than expected. Cheers! :)
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