Small angle neutron scattering measurements were made on a series of block copolymer micelles that represent model systems for spherical polymer brushes. We find hyperbolic density profiles of the form ${r}^{\ensuremath{-}\ensuremath{\alpha}}$ with values of $\ensuremath{\alpha}$ between 1.05 and 1.35. This as well as the scaling of the brush height with the aggregation number $f$ are in agreement with the model proposed by Daoud and Cotton [J. Phys. (Paris) 43, 531 (1982)] for unswollen and swollen spherical polymer brushes.