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Volume of a solid using shells

  1. Sep 23, 2013 #1
    1. The problem statement, all variables and given/known data

    Find the volume of the region bounded by the curve y=x^(1/3) and y=x rotated about the line y=1.

    2. Relevant equations

    3. The attempt at a solution
    My teacher's solution is 4∏/15 . I got 11∏/210.

    http://imageshack.us/a/img443/426/0zhs.jpg [Broken]
    http://imageshack.us/a/img443/426/0zhs.jpg [Broken]
    Where am I going wrong?
    Last edited by a moderator: May 6, 2017
  2. jcsd
  3. Sep 24, 2013 #2


    Staff: Mentor

    You don't have a sketch of the solid of revolution, so I can't tell what you did. However, it looks like you didn't rotate the region around the line y = 1. I find that it's helpful to have a sketch of the solid, at least a cross-section of it, showing the typical volume element.
    Last edited by a moderator: May 6, 2017
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