We have performed Monte Carlo computer simulations of a fluid of overlapping hard spheres inside a spherical cavity. The model of the interparticle potential is that introduced by Cummings and Stell [Mol. Phys. 1984, 51, 253]. Our investigations are concentrated on the evaluation of the structure of the fluid at the interface and on the evaluation of the orientation of the dimers in particular. Moreover, we have performed similar simulations for the fluid in contact with a hard wall. In the latter case, and also in the case of some confined systems, we have also applied the singlet theory equations to calculate the total density profiles.