Spheres are to one another in the triplicate ratio of their respective diameters.
Proof
Apply the method of exhaustion: inscribe similar polyhedra (XII.17);
by XII.12 (similar cones) and the polyhedron's similar-pyramid
decomposition, the inscribed solids are in the triplicate ratio of
diameters. By X.1 the inscribed solids approach the spheres in
volume; the limit gives the result.