Epithelia are tissues which envelop organs, exchange with and protect from their environment. The tight packing of cells within an epithelium guarantees its cohesiveness and impermeability, essential to its functions. Yet, how cells spatially arrange in three dimensions within an epithelium, and how the three-dimensional cell packing responds to geometrical constraints, is not fully understood. In a proliferating epithelium, cellular volumes vary from cell to cell, notably due to cell growth. At the same time, epithelia tend to display a smooth, continuous apical surface, indicating that cell shape determinants are spatially coupled. It is unclear how these and other factors modulate cell shape variability within the epithelium. Here, we segmented three-dimensional cell shapes of MDCK epithelia, grown in hollow spheres of alginate. With this assay, we could modulate the substrate adhesive properties, tissue curvature, and cell area density. We observed that as the tissue proliferates and cell density increases, average cell volume decreases. In contrast, cell height is relatively conserved over time, with an average value sensitive to the rigidity, curvature and adhesive strength of the substrate. We identified large and spatially correlated fluctuations in cell skewing, defined as the relative difference between apical and basal area that do not arise from curvature. Skewing is associated to spatial patterns of tilted cells whose apico-basal axis deviates from orthogonality to the substrate. Surprisingly, cell skewing and cell height are correlated, indicating internal rules for three-dimensional cell shapes. Altogether, our study identifies unexpected patterns of three-dimensional cell shape variation within a proliferative epithelium.