We investigate a mean filed theory to elucidate the fraction of hard spheres in the rim of rigid spherical cavities for densities similar to crowded cellular nuclei. Rims are one hard sphere thickness from the interior surface of cavities. We theoretically interpret the particle fraction around the rim by considering entropies from inter-particle excluded volume interactions and depletion forces under confined cavities. By adapting the characteristic length of depletion forces as a single tunable parameter, the proposed theory is successfully applied to understand simulation data, which provides a simple but general picture on confinement effects including cavity curvature and density. (C) 2013 Elsevier B. V. All rights reserved.