The size dependence of whispering gallery modes in dielectric resonators with hexagonal cross section has been observed within the visible spectral range for cavity diameters comparable to the light wavelength. As a model system single, tapered, high aspect ratio zinc oxide nanoneedles were analyzed. They enable systematic investigations as a function of the resonator diameter down to the nanometer regime. A simple plane wave interference model without free parameter describes the spectral positions and the linewidths of the modes in good agreement with the experiment.