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                                      Michael Lee's Mathematics and Physics

Volume of Various Tori. (see also Surface Area of a Torus for more information).

  1. Washer Method
  2. Volume of the Frustum of a Torus
  3. Ring Method
  4. Volume of a Torus with the sides "shaved off." 

 

Examine the following cross sectional diagram of a ring or horn torus.

 

 

 

 

 Method I. (Washer Method)

 

 

Volume of a Frustum of a Torus

 

 

 

 

 

 

 

 

 Method II. Ring Method

 Again the diagram above.

 

 

 

               That equation is for a full torus only. 

 

 

 

The Volume of a Torus with the sides "shaved" off

 The two sides of a torus can be "shaved" off as shown.