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Crossing plane and cuboid

• To: mathgroup at smc.vnet.net
• Subject: [mg30236] Crossing plane and cuboid
• From: seidovzf at yahoo.com (Zakir F. Seidov)
• Date: Fri, 3 Aug 2001 00:56:05 -0400 (EDT)
• Organization: The Math Forum
• Sender: owner-wri-mathgroup at wolfram.com

Some times ago I thought on a lot 
but could not find solution for the problem:
we have a cuboid (= parallelepiped) with edges a, b, c;
such that 0<x<a, 0<y<b, 0<z<c;
also we have a plane:
X/A + Y/B + Z/C = 1.

Values a, b, c, A, B, C are such that 
plane crosses cuboid for sure, 
.....................========

and I don't need generalized program 
checking all weird cases...

What I need is a Mathematica program to calculate: 
 a) volumes of two parts of cuboid  
 b) area of cross-section

May be our dear Mathematica gurus
(I mean dear Mathematica and dear gurus) 
can provide me with it.

Thank you very much.
Zakir

PS For more patient/interested people:
This is for the classical and unsolved yet 
(according to Michael Trott) 
problem of random tetrahedron in cube. 
For more easy problem
of random triangle in square see

[1] M. Trott, Mathematica J., v7, i2, 189-197, 1998 
[2] me, http:arxiv.org/abs/math.GM/0002134