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Homework Help: Cylindrical Shells Volume

  1. Oct 13, 2011 #1
    1. The problem statement, all variables and given/known data

    Using cylindrical shells, find the volume obtained by rotating the region bounded by the given curves about the x-axis.

    x= (y^2) +1

    x= 0



    2. Relevant equations

    2∏ ∫ rh

    3. The attempt at a solution

    2∏ ∫ from 1 to 2 (y^2) + 1

    I'm not sure where to go from here. :S Please help.
  2. jcsd
  3. Oct 13, 2011 #2


    Staff: Mentor

    Start with a sketch of the region that is being rotated. Then draw a sketch of the solid that is formed.
  4. Oct 13, 2011 #3
    I drew a sketch. I'm not sure what do do about the radius part. I know y= 2 is the higher radius along the x-axis. And y= 1 is the lower radius along the x-axis. Do I subtract the radius minus function?
  5. Oct 13, 2011 #4


    Staff: Mentor

    The expression for incremental volume (the volume of a thin horizontal strip that is revolved around the x-axis) is 2[itex]\pi[/itex] * radius * width of strip * Δy.

    The radius varies from what to what?
    How wide is a typical strip?
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