Another 3D-printing suggestion from Colm Mulcahy:

Archimedes proved that if you slice a sphere of radius r with two planes a distance h apart, the surface area is 2πrh—the same as a cylinder of the same radius and height. So, it doesn't depend on where the slicing occurs.
1/2

Idea: Produce 3D-printed slices of a (hollow) sphere, all of the same height. Print with 100% fill. They should all weigh the same.

Bam!

I just put these files on Thingiverse for anyone to download and print https://www.thingiverse.com/thing:7305536