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From: "Pinpress " <nospam__@yahoo.com>
Newsgroups: comp.soft-sys.matlab
Subject: Re: volume of a pyramid
Date: Fri, 23 Nov 2007 03:05:56 +0000 (UTC)
Organization: University of Pennsylvania
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First, thanks for the reply.

As for the volume, it is a solid that both radial surfaces
have identical radius toward a common origin.  All other 4
surfaces are on a straight plane (as opposed to the two
radial surfaces), and their angles with the vertical axis is
known (i.e.g, vector-to-plane angles are known). 

So are your equations supposed to calculate the solid volume
as describe above.  I will examine the equations too. 
Thanks again. 

> --------
>   You haven't stated explicitly what shape your image has.
 It looks like a solid 
> defined by projecting a spherical quadrilateral surface
inwards along radial 
> lines to a smaller spherical quadrilateral.  Is that correct?
> 
>   If so, then its volume can be calculated in terms of the
area of the outer 
> quadrilateral:
> 
>  V = a*R/3*(1 &#8211; (r/R)^3)
> 
> Where R is the outer radius, r the inner radius, and a the
outer area.
> 
>   As for computing a, it is equal to
> 
>  a = R^2*(A + B + C + D &#8211; 2*pi)
> 
> where A, B, C, and D are the four angles in radians at the
four vertices of the 
> outer quadrilateral.
> 
>   So your problem becomes that of determined what those
four angles are.  
> There is no way of determining them without additional
information about 
> that quadrilateral.
> 
> Roger Stafford
>