Final answer:
Marcel's first mistake was assuming that Cavalieri's principle could be applied to equate the volumes of a cylinder and a cone, which overlooks the fact that the cross-sectional areas at corresponding heights are not equal in a cone, unlike in a cylinder.
Step-by-step explanation:
The first mistake that Marcel made was incorrectly applying Cavalieri's principle to a cylinder and cone. While it is true that the volume of a cylinder is the cross-sectional area (A) times the height (h), as given by the formula V = Ah, a cone's volume is only one-third of the volume of a cylinder with the same base area and height. Cavalieri's principle states that two solids with corresponding cross-sections of equal area at equal heights have the same volume, but it only applies when all corresponding cross-sections are equal. Although the base areas of the cylinder and the cone are the same, the areas of the cross-sections at different heights are not the same due to the cone's tapering shape.