The specific area of the solid-liquid interface is an important integral measure for the morphological evolution during solidification. It represents not only the inverse of a characteristic length scale of the microstructure, but it is also a key ingredient in volume- averaged models of alloy solidification. Analytical descriptions exist for either pure coarsening or pure growth processes. However, all alloy solidification processes involve concurrent growth and coarsening. In the present study, the kinetics of the solid-liquid interface of a columnar dendrite are studied using a 3D phase-field model. The simulation results are combined with data from recent experiments to study the influence of the cooling rate on the evolution of the interfacial area.