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Homework Help: Volume of the solid using a cylindrical cross section

  1. Aug 1, 2012 #1
    [STRIKE][/STRIKE]1. The problem statement, all variables and given/known data
    Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified axis.

    2. Relevant equations

    [itex]y = \sqrt{x-1} , y = 0, x = 5;[/itex] about [itex]y = 3[/itex]

    3. The attempt at a solution
    I already completed graphing it, but not really sure how to show that here.

    2[itex]\pi[/itex][itex]\int_0^2[/itex](shell radius)(shell height) [itex]dy[/itex]
    2[itex]\pi[/itex][itex]\int_0^2[/itex][itex](y)(y^2+1)[/itex] [itex]dy[/itex]
    2[itex]\pi[/itex][itex]\int_0^2[/itex][itex](y^3+y)[/itex] [itex]dy[/itex]
    [itex]2\pi (((y^4)\div4)) + (y^2)\div2)[/itex]
    [itex]2\pi(4+2) - 0[/itex]

    Is that correct? I'm not sure if I did the shell height correctly.
  2. jcsd
  3. Aug 1, 2012 #2


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    Science Advisor

    You are rotating around y= 3 which means that the axis of each cylinder is y= 3 and the radius is 3- y, not y.
  4. Aug 1, 2012 #3
    Aha, thank you so much! :)
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