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Formula to calculate toroidal volume/surface area
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Charl du Plessis
Feb 5, 1998, 3:00:00 AM2/5/98
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Help - in search of formulae to calculate the surface area and volume of a
torus
and if possible a way of determining optimum relationship between volume
and surface area
i.e. min surface for max vol
any help gratefully received
Charl du Plessis
José H. Nieto
Feb 5, 1998, 3:00:00 AM2/5/98
to
In article <01bd3266$bb34e1e0$91401fc4@charldup>,
"Charl du Plessis" <char...@iafrica.com> wrote:
>
> Help - in search of formulae to calculate the surface area and volume of a
> torus
> and if possible a way of determining optimum relationship between volume
> and surface area
>
> i.e. min surface for max vol
Suppose that the torus is generated by rotating a circle of radius r and
center Q around an axis belonging to its plane at a distance R>=r of Q.
Then the volume and area are given by
V = 2*Pi^2*R*r^2 A = 4*Pi^2*R*r
If the volume V is given then the area may be arbitrarily large: just
take r small and R = V/(2*Pi^2*r^2). The minimum area is obtained when
R = r = cube root of V/(2*Pi^2).
José H. Nieto
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Apr 18, 2013, 3:36:08 AM4/18/13
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Dealers, distributors, agents, wholesalers are recruiting currently. If you interest pls let us know.
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Web: www.jinaipu.com/ www.app-one.com.cn
Tel.: 0086-10-82133318 Ext.810
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