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enter image description here

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? enter image description here

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    $\begingroup$ It's impossible for us to answer whether the two figures have equal cross sections, since their explicit forms are unspecified. They may or may not be; we cannot know. As to whether Cavalieri's principle is appropriate in this application, that depends, as you've noted, on whether the cross sections are equal, which is an assumption of the model that can only be supported with empirical evidence. $\endgroup$
    – Jam
    Commented Oct 17, 2022 at 12:59
  • $\begingroup$ As I've said the cross sectional area of outer surface (at every z) in two cases are equal. The lower surface in two cases is at a similar distance to the above surface. So it seems that the lower surface is completely specified. And now I want to know whether the volume between the two surfaces in two cases are equal or not? $\endgroup$
    – Dweller on threshold
    Commented Oct 18, 2022 at 4:51

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