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Homework Help: Using polar coordinates to find the volume of the given solid

  1. Apr 2, 2010 #1
    1. Use polar coordinates to find the volume of the given solid.



    2. Inside the sphere x^2 + y^2 + z^2 = 16 and outside the cylinder x^2 + y^2 = 4.
     
  2. jcsd
  3. Apr 2, 2010 #2

    Mark44

    Staff: Mentor

    What have you tried? You have to show an effort first.
     
  4. Apr 2, 2010 #3
    I've tried doing a double integral from theta=0 to theta=2pi and r=0 to r=4 of ((16-r^2)^(1/2))r (dr)(dtheta)
     
  5. Apr 2, 2010 #4

    Mark44

    Staff: Mentor

    The limits of integration for r should be from r = 2 to r = 4. If you go from r = 0, you're getting the volume inside the cylinder, which you don't want.
     
  6. Apr 2, 2010 #5
    Ok. Is the actual integral correct?
     
  7. Apr 2, 2010 #6

    Mark44

    Staff: Mentor

    Yes, I don't see anything wrong with it.
     
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