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Homework Help: Volume of generated solid by rotation

  1. Sep 23, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the volume of the solid generated where y = 1/x for 1<=x<=5 is rotated about the x axis.

    2. Relevant equations

    I = r^2 dm, sqrt(1 + (dy/dx)^2) dx,

    3. The attempt at a solution

    So I have found the length of the curve and can henceforth find surface area and so on but I cannot figure out the step to take to get to volume, I understand that it probably isnt too difficult after the first part, so does anyone knw what the relevant formula is to solve for this, any help much appreciated :) btw solid will b the shape of a spinning top in a way ty :)
     
  2. jcsd
  3. Sep 23, 2010 #2
    Hi again Ombudsmand,

    The first thing that I notice here is

    [tex]I = \int r^2 dm[/tex] which is the definition of the moment of ineteria..


    Look this up in the Calculus bible and you will find what you are looking for..
     
    Last edited: Sep 23, 2010
  4. Sep 23, 2010 #3
    hey :) Is ther really a calculus bible online?? lol but i cant find it in my textbook and all ones i find online are specific to certain shapes but im sure that like the third integral or something like tht hsould do it. I can find the area under the curve then i know i have 2pi degrees of rotation but how to put that into volumetric terms within the given bounds? thanks again for helpin me out
     
  5. Sep 23, 2010 #4
    Edwards and Penney....

    Roting a solid about a fixed axis..

    Should be a bell Ring :)
     
  6. Sep 23, 2010 #5
    hmmm perhaps all i need is (pi) integral of (f(x))^2 dx, ill give it a shot and see what happens
     
  7. Sep 23, 2010 #6
  8. Sep 23, 2010 #7
    lol! de ja vu frm reading that lol, well i used (pi) integral of (f(x))^2 dx and got the correct answer so all looks well. Thanks heaps again u r really good at helping ppl saved me twice tonite already! have a good one suz :D
     
  9. Sep 23, 2010 #8
    You are welcome :)
     
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