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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.