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Triple Integration Help

  1. Apr 26, 2009 #1
    1. The problem statement, all variables and given/known data
    Sketch the solid B that lies inside the surface x^2 + y^2 = 1 and is bounded above and below by the surface x^2 + y^2 + z^2= 2^2. Then find the volume of B.


    2. Relevant equations

    projxy = projection onto the xy plane, proj zy = projection on the zy plane

    3. The attempt at a solution
    (See attached)

    http://img511.imageshack.us/img511/440/chibusq.jpg [Broken]

    I just wanted to check whether my definition of the integration is correct, meaning:

    1) Is the function of the integration right? (Since the circle on the xy plane is x^2 + y^2 = 1, i've used that)

    2) Are the limits correct?

    Thanks for any help!
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Apr 26, 2009 #2
    Any help?

    I've converted the above integral into cylindrical coordinates and solved it, and I ended up with Pi*sqrt(3) as the solution. However, it doesnt match the answer of solving the cylinder by using the formula V(cyl)=pi*r^2*h = pi*(1)^2*2*sqrt(3) = pi*2*sqrt(3)
     
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