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So I place spheres of radius chosen at random from a normal distribution of known mean and standard deviation in a cub or cuboid at random (not overlapping) until a known density of the entire cube is reached.

If I cut through the cuboid at a random location perpendicular to one axis what volume of spheres will be opened to the surface (think edge of a swiss cheese) on average. So I mean just the bits of the spheres that are in one side or the other, not the total volume of the spheres dissected.

edit:Currently I can sort of brute force the answer by running a simulation, but its not as elegant as I would like

Cheers!

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    $\begingroup$ Welcome to Math.SE. This is a very interesting question. Did you put any thought into it so far? $\endgroup$
    – AlexR
    Aug 14, 2014 at 12:57
  • $\begingroup$ Well, I've actually written a function in matlab to do it (an algorithm calculates the sphere's radius and places all the spheres in the cube then makes the cuts and measures the volume exposed). But it takes a while to place the spheres so I started looking at ways of calculating it mathematically. I started getting the points together to fit some regressions but ultimately I don't have time to run all the simulations, so at that point I figured the internet might find it interesting, and I don't know enough about maths to know where to begin. $\endgroup$
    – Tom
    Aug 14, 2014 at 13:44

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