  In various stereological problems an $n$-dimensional convex body is
intersected with an $(n-1)$-dimensional Isotropic Uniformly Random (IUR)
hyperplane. In this paper the cumulative distribution function associated with
the $(n-1)$-dimensional volume of such a random section is studied. This
distribution is also known as chord length distribution and cross section area
distribution in the planar and spatial case respectively. For various classes
of convex bodies it is shown that these distribution functions are absolutely
continuous with respect to Lebesgue measure. A Monte Carlo simulation scheme is
proposed for approximating the corresponding probability density functions.
