Abstract: Semiempirical nuclear binding energy formula systematizes the dependence of nuclear energies on the neutron and proton content of nuclei.  Due to the short-range nature of nuclear interactions, to first order, the binding energy is proportional to the nucleon number or, equivalently, the nuclear volume. Corrections for the surface, where nuclear interactions weaken, for the Coulomb repulsion between protons, and for the effects of a difference between the proton and neutron numbers all reduce nuclear binding.  Recent development of the beams of short-lived nuclei led to the interest in nuclei with an unusually high neutron or proton content.  In this context, we examine
the term for asymmetry between protons and neutrons in the binding formula, proportional to nuclear volume in the standard expression.  We point out that a proper description of the binding energies for light nuclei requires an inclusion of a surface asymmetry term in the formula.  With such a term, the nuclear surface and interior compete for the asymmetry between protons and neutrons.  The asymmetry in the surface results in different radii for nuclear proton and neutron distributions,
in accordance with measurements.  Using data on energies and on radii, we constrain the volume and surface asymmetry terms in the binding formula and infer, further, constraints on the density dependence of nuclear interactions.  The volume and surface terms impact nuclear excitations corresponding to asymmetry oscillations.