Cavalieri's Principle

1. If the lengths of every one-dimensional slice are equal for two regions, then the regions have equal Areas.

2. If the Areas of every two-dimensional slice (Cross-Section) are equal for two Solids, then the Solids have equal Volumes.

See also Cross-Section, Pappus's Centroid Theorem

References

Beyer, W. H. (Ed.) CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 126 and 132, 1987.