Definition of a sphere If there is no further specification (such as solid or hollow), does a "sphere" refer to the solid/filled form or the hollow shell? Thanks.

In mathematics, the word "sphere" refers to the hollow shell (see here). The word "ball" is reserved for the solid version (see here).

So, for example, the unit **sphere** in $\mathbb{R}^3$ is equal to the set $$\\{(x,y,z)\in\mathbb{R}^3\mid x^2+y^2+z^2=1\\}$$ while the unit **ball** in $\mathbb{R}^3$ is equal to the set $$\\{(x,y,z)\in\mathbb{R}^3\mid x^2+y^2+z^2\leq 1\\}.$$

In common usage of the word "sphere" in English, it could mean either.