I finally got around to shedding my library of CD cases (I know, I’m quite behind), but it got me thinking about Cavalieri’s Principle.
Cavalieri’s Principle essentially states that if two prisms have the property that all corresponding cross sections have the same area, then those prisms have the same volume.
For instance, here we have two stacks of CD cases. Every cross-section of each “prism” here is a single CD case. Since corresponding cross-sections always have equal area, Cavalieri’s Principle tells us that these prisms have equal volume, even though one of the stacks is oblique.
Here’s another demonstration of Cavalieri’s Principle using the CDs themselves.