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Unformatted text preview: The comparison is below. At a height h from the center of the figures we get the following cross sections. A 1 ( h ) A 2 ( h ) h V 1 V 2 b a torus 2 ! b 2 a cylinder b + a 2 ! h 2 b ! a 2 ! h 2 2 b 2 a 2 ! h 2 So, the area for the torus is A 1 ( h ) = ! b + a 2 " h 2 ( ) 2 " b " a 2 " h 2 ( ) 2 = 4 b a 2 " h 2 . The area for the cylinder is clearly A 2 ( h ) = 4 b a 2 " h 2 . So, A 1 ( h ) = A 2 ( h ) for every h . This implies that the volumes are the same. So, the volume of a torus is given by the following. V = 4 2 ba 2...
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 Spring '07
 JURY
 Calculus, Prism

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