Summary: Starting from a homogeneous perfect fluid with \(\rho =\rho (t)\) and \(p=p(t)\), we find that the Friedman-Robertson-Walker-type of metric is the unique solution for the higher dimensional spherically symmetric line-element. It is a generalization in the sense that, when the number of dimensions becomes four, the ‘standard’ FRW metric results. Assuming an equation of state \(p=m\rho\), the explicit solutions of the scale factor are found and its cosmological implications discussed. Some astrophysical parameters are calculated and a comparison made with the analogous four-dimensional cases. Further, we extend to the case of higher dimensions an earlier result of J. Eisenstaedt and N. O. Santos [Astrophys. J., 337, 601-602 (1989)] that the mean density of a four-dimensional local spherical inhomogeneity on a FRW universe should necessarily be equal to the cosmological energy density.