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Message from discussion finding volume of a torus
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Pubkeybreaker  
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 More options Nov 4 2009, 9:01 pm
Newsgroups: sci.math
From: Pubkeybreaker <pubkeybrea...@aol.com>
Date: Wed, 4 Nov 2009 13:01:09 -0800 (PST)
Local: Wed, Nov 4 2009 9:01 pm
Subject: Re: finding volume of a torus
On Nov 4, 11:43 am, aegis <ae...@mad.scientist.com> wrote:

> I have the circle (x-1)^2 + y^2 = 1 and I'm rotating it
> around the y-axis.

> dV = 2*pi*x * h(x) dx

> where h(x) = 2*sqrt(1 - (x - 1)^2 )

> integrating from 0 to 2, I end up with
> pi^2.  Does this come out right?

Thm:
The volume will equal the cross-sectional area
times the distance travelled by the centroid of
the cross section as you rotate it.

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