Survival of mammalian cells is achieved by tight control of cell volume while transmembrane potential is known to control many cellular functions since the seminal work of Hodgkin and Huxley. Regulation of cell volume and transmembrane potential have a wide range of implications in physiology, from neurological and cardiac disorders to cancer and muscle fatigue. Therefore understanding the relationship between transmembrane potential, ion fluxes, and cell volume regulation has become of great interest. In this paper we derive a system of differential equations that links transmembrane potential, ionic concentrations, and cell volume. This model demonstrates that volume stabilization occurs within minutes of changes in extracellular osmotic pressure. We infer a straightforward relationship between transmembrane potential and cell volume. Our model is a generalization of previous models in which either cell volume was constant or osmotic regulation instantaneous. When the extracellular osmotic pressure is constant, the cell volume varies as a function of transmembrane potential and ions fluxes thus providing an implicit link between transmembrane potential and cell growth. Numerical simulations of the model provide results that are consistent with experimental data in terms of time-related changes in cell volume and dynamics of the phenomena.