Final answer:
Cavalleri's principle says that solids with equal heights and cross-sectional areas at every level have the same volume, which is evident from the formula for volume, V = Ah.
Step-by-step explanation:
Cavalleri's principle states that if two solids have the same height and the same cross-sectional area at every level parallel to their bases, then they will have the same volume. This principle is a consequence of how volume is calculated for three-dimensional objects. For example, the volume of a cylinder can be found using the formula V = Ah, where A is the cross-sectional area, and h is the height. If two solids share the same values of A and h for every cross-section throughout their height, their volumes will consequently be equal. This concept is crucial in understanding geometric properties and in real-world applications like fluid displacement in physics.