This paper describes a new method for estimating particle volume distributions using isotropic, uniform, random (IUR) sections. An attractive feature of the method is that it makes no assumptions about the shape of the particles. Since IUR sections do not uniquely determine the volume distribution for particles of general shape, the method takes a probabilistic approach. It uses the principle of maximum entropy to determine the most likely distribution given the available information. This information is extracted from the sections using geometric probability. The algorithm was tested on simulated ellipsoids, with excellent results.