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Volume generated by curve

  1. Jul 15, 2006 #1
    The question is

    Given a curve C whose equation is give by y=(12/(x + 3))- 4,
    find the region bounded by C, the line x=0, the line x=3 and the line y=8 is rotated through 360 degree about the y-axis. Calculate the exact value of the volume generated.

    My solution is here
    http://www.geocities.com/myjunkmail31/Volume.jpg

    However, this solution is not the answer in the textbook. The anwser in the textbook is
    36pi(1+2ln2).
    Can someone show me where am I doing wrong?
     
    Last edited: Jul 15, 2006
  2. jcsd
  3. Jul 15, 2006 #2

    benorin

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    Homework Helper

    The error is in V1: Easy fix: [tex]V_1 = \pi 3^2 (2) - \pi (54 - 2 ln 2)[/tex].

    The volume you calculated is that of the solid generated by rotating the region between the given curve and the y-axis about the y-axis, but you wanted to rotate the region between the given curve and x=3 about the y-axis. So just subtract what you got for V1 from the volume of the cylinder of radius 3 with height 2.
     
  4. Jul 15, 2006 #3
    Awesome, very thanks=)
     
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