[algorias]

If you talk about the "volume of a sphere" (like the article does), then a sphere embedded in 3 dimensions should be 3 dimensional. This would usually be called a ball and not a sphere, though.

Note that analogously, a cube in 3 dimensional space is always considered to be 3 dimensional.

[OscarCunningham]

Right, the 2-sphere is the surface of the 3-ball. I think "volume of a sphere" is okay though. It just means the volume enclosed.

>a cube in 3 dimensional space is always considered to be 3 dimensional.

So "cubes" are taken to include their interior. That makes sense I suppose. I wonder what the surface of a cube is called. A "box" maybe?