  In this paper we investigate relationships between the volumes of cells of
three-dimensional Voronoi tessellations and the lengths and areas of sections
obtained by intersecting the tessellation with a randomly oriented plane. Here,
in order to obtain analytical results, Voronoi cells are approximated to
spheres. First, the probability density function for the lengths of the radii
of the sections is derived and it is shown that it is related to the Meijer
$G$-function; its properties are discussed and comparisons are made with the
numerical results. Next the probability density function for the areas of cross
sections is computed and compared with the results of numerical simulations.
