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!