We observe that a density-depleted vortex core evolves into concentric density ripples in a freely-expanding quasi-two-dimensional Bose-Einstein condensate. The atomic density of the expanding condensate rapidly reduces due to the fast expansion along the tightly confined axial direction; thus, the transverse expansion of the condensate is not significantly affected by atom-atom interactions. We find that the observed density profiles of the vortex cores are in good quantitative agreement with numerical simulations assuming no interactions. We analyze the defocused images of the vortex cores, where defocussing is caused by the free fall of the condensate during the expansion time. In the defocused images, the vortex core becomes magnified and appears to be filled after a certain expansion time that depends on the vortex charge number.