In this paper, we present a physical modeling activity whose objective is to allow students to determine the differences between a disk and a sphere using pure scientific criteria. Thereunto, we reproduce the Sun-Earth-Moon system with low-cost materials and compare the illumination effects on the Moon considering two possible shapes for it (a sphere and a disk). The analysis is based on the shape of the terminator line produced in each case as a function of the illumination angle. The results obtained are first discussed and then applied so that one can interpret the observed patterns in the illumination effects of other celestial bodies, such as Venus or even the Earth. Thereby, the activity can be very useful to unmask the unscientific idea of flat Earth. The entire activity is easily replicable and it may be useful to promote a more realistic view of science and its methods.