Prove volume of a torus equation

  • Thread starter brandy
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  • #1
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Main Question or Discussion Point

how does the formula for volume of a torus work.
is there a proof with integration??

could you use an ellipse?
 

Answers and Replies

  • #2
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It's a surface of revolution, so yes, there is a formula (method of cylindrical shells).
 
  • #3
tiny-tim
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how does the formula for volume of a torus work.
is there a proof with integration??
Hi brandy! :smile:

Yes, slice it into horizontal rings (or vertical discs), and integrate. :wink:
could you use an ellipse?
uhhh? :confused:
 
  • #4
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by ellipse i mean, an ellipse is revolved around a circular ring.
sort of like taking a torus and stretching it upward...
get me?
 
  • #5
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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?
 
  • #6
tiny-tim
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by ellipse i mean, an ellipse is revolved around a circular ring.
sort of like taking a torus and stretching it upward...
get me?
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?
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:
 
  • #7
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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.
 
  • #8
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i mean like wat do u do to the points.... to get the volume of revolution
 
  • #9
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Have you considered using Pappus' centroid theorem?
 

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