If I have a closed, simply connected region in the $z$-plane, and I 'extrude' this region vertically by a height $h$, what is the relationship between the curved surface area and the volume of the extrusion?
2026-03-26 17:34:32.1774546472
Is there a relationship between the curved surface area of an extruded region and its volume?
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Green's theorem is something like this for 2 dimensions. I don't know if it has a 3D version. But I found this