An Optical Illusion of Volume Promoted by the Transformation of a Paper Model from a Square Prism to a Tetrahedron

During the recycling of a cardboard box in the shape of a right prism with a square base to build a tetrahedron, there was the curious coincidence that the height of the first was equal to the inclined height of the second. After some bending and cutting on the prism, its dynamic conversion to the tetrahedron and vice versa was achieved. This fact motivated us to carry out a study on the meaningful learning of a small group of participants (N = 10) with minimum primary school education, regarding the volume of these two common geometric bodies. It was found that 70 % of the study population thought that the volumes were equal and that 100 % had forgotten the formula to calculate the volume of the tetrahedron. A template to build the model and a video to illustrate the mentioned transformation process are also presented.