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A density functional theory of the spatial distribution and biaxial nematic order of polymers of arbitrary length and rigidity inside a spherical cavity is proposed. The local order of different chain segments is considered as an alignment to a spatially varying director field of cylindrical symmetry. The steric interactions are taken into account in the second virial approximation. Polymer density and orientational order distributions inside the spherically cavity are the principal results. It was found that short and flexible polymers were located at the center of the sphere and were orientationaly disordered. Upon increasing polymer length and/or polymer rigidity, the location of the polymer was continuously shifted toward the surface of the spherical cavity and the polymer segments became gradually more aligned. Parameters have been selected to model the behavior of genomes in spherical viral capsids.