Solving the hydrodynamical equations by means of a variational principle, we obtain a simultaneous description of the surface and volume modes of the valence electrons in a metal. This variational scheme, which has been previously used in the context of nuclear fluid dynamics, is applied to describe the dynamics of the valence electrons in a spherical metal cluster and of the valence electrons in the metal surrounding a spherical cavity (void). The eigenmodes fulfil the linear energy-weighted sum rule , the inverse energy-weighted sum rule and orthogonality relations. The surface modes predicted by Mie (in clusters) and by Natta (in cavities) appear in this model as natural solutions of the equations of motion and boundary conditions. We have considered a stabilized spherical jellium model. The parameters of the effective interaction are obtained by means of a variational method taking into account the experimental values of the density, compressibility and bulk energy. In the present model we have ignored the diffuseness of the equilibrium electron density, taking into account, however, the surface degrees of freedom of the valence electrons and thus allowing them to penetrate into the vacuum (outside of the jellium) when undergoing collective oscillations. The spectra of the excitation energies, and the electronic transition currents and transition densities are obtained for spherical clusters and voids.