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Prove volume of a torus equation

  1. Apr 28, 2009 #1
    how does the formula for volume of a torus work.
    is there a proof with integration??

    could you use an ellipse?
     
  2. jcsd
  3. Apr 28, 2009 #2
    It's a surface of revolution, so yes, there is a formula (method of cylindrical shells).
     
  4. Apr 28, 2009 #3

    tiny-tim

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    Hi brandy! :smile:

    Yes, slice it into horizontal rings (or vertical discs), and integrate. :wink:
    uhhh? :confused:
     
  5. Apr 29, 2009 #4
    by ellipse i mean, an ellipse is revolved around a circular ring.
    sort of like taking a torus and stretching it upward...
    get me?
     
  6. Apr 29, 2009 #5
    also what could you use a shape like a polygon or something and revolve it around a circle.

    how could you would out the volume?
     
  7. Apr 30, 2009 #6

    tiny-tim

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    ah! got you! :smile:

    yes, you can use any cross-section shape …

    if you slice it into horizontal rings, you just need to know the width of the polygon at each height …

    and if you use vertical discs, you just need to know the height of the polygon at each width :wink:
     
  8. Apr 30, 2009 #7
    sorry. i kept rewording what i was going to say and i didnt read what i wrote.
    so all you need is the x,y positions ???
    can you explain how this works??
    keep in mind i know nothing AT ALL.
     
  9. Apr 30, 2009 #8
    i mean like wat do u do to the points.... to get the volume of revolution
     
  10. May 2, 2009 #9
    Have you considered using Pappus' centroid theorem?
     
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