In petroleum engineering, for easier calculation of the volume underlying a specific surface underground, the irregular surfaces are modeled by an equivalent surface with circular cross sections, which is constructed based on Cavalieri's Principle. For example, the above picture shows a (anticline) surface which connects to another (fault) surface. An equivalent surface is constructed that in every z (depth) has a circular cross section with equal area compared to the cross sections of similar depth in original surface. The volume underlying these two surfaces down to a specific depth is apparently equal based on Cavalieri's Principle. And now my question is about the equivalence of volume of layers of equal thickness underlying the surfaces depicted in the picture below. Whether they are equal or not?
