Academy of Sciences of Heroesland

I prefer to call the sphere three-dimensional

And I prefer to call it a pot... You are confusing a sphere with a ball, sir.;) A body cannot have the same dimensionality as the surface that bounds it. The bounding surface has a dimensionality 1 lower. Three-dimensional objects have volume, whereas two-dimensional ones have area. I've seen the formula for the area of a sphere, but I haven't seen a formula for its volume.