The sizes of three-dimensional particles at a microscopic level reveal properties at a macroscopic level for many applications in materials science, but can be difficult to measure. This thesis builds on existing methods that estimate the size distribution of such particles of the same three-dimensional shape, using information obtained from their profiles in two-dimensional cross-sections. This is a well-known stereological problem. An existing method is explained, which yields a maximum likelihood estimator based on the two-dimensional sizes of observed profiles. This method is expanded, resulting in a new maximum likelihood estimator, which is based on the paired two-dimensional sizes and shapes of the observed profiles. The performance of both the existing and the new estimators is analysed in simulations, as well as in an application to real data obtained from a steel microstructure. By comparing the performances of both estimators, this thesis aims to answer whether or not the additional shape-related information improves the resulting estimator. Its conclusions are that the new estimator performs better on average than the existing estimator, but not in general. Moreover, the new estimator only performs better in applications when the observed information is accurate, which is not always the case.