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Homework Help: Finding the Volume

  1. May 23, 2005 #1
    Hey everyone...I need to find the volume of the following shape...

    [tex] y= \frac{1}{x}, y=0, x=1, x=3[/tex]

    rotated about [tex] y=-1 [/tex]

    ok so, i drew out the shape, and for the radius i came up with:

    [tex] r= \frac{1}{x} + 1 [/tex]

    I think thats correct...so assuming that my radius is right, then the volume would be...

    [tex] \pi \int_{1}^{3} ( \frac{1}{x} +1)^2 dx [/tex]

    did i set this up right? Thanks..
  2. jcsd
  3. May 24, 2005 #2
    http://tutorial.math.lamar.edu/AllBrowsers/2413/VolumeWithRings.asp [Broken]

    Check out examples 3 and 4.
    Last edited by a moderator: May 2, 2017
  4. May 24, 2005 #3


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    Your solid has a hole in the middle. The y = 0 boundary excludes a cylinder of radius 1 from the solid. You need the difference of the squares of the outer radius and inner radius.
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