I am looking for a text where "solid" is given a formal definition. I have looked at http://mathworld.wolfram.com/Solid.html and the definition referenced there from Kern and Bland ("any limited portion of space bounded by surfaces") is the type of thing I'm looking for, but I cannot find the text online or for sale, so a more accessible resource would be appreciated.
Edit: Instead of a reference, maybe someone could help with my confusion. If we have 2 non-intersecting balls, that is certainly a limited portion of space bounded by surfaces. But would most people consider this a geometric solid? If not, what should be required of the space topologically?
Historically this just mimic the original definition of polyhedron: a limited portion of space bounded by planes. Which, accordingly, implies that a cube from which you remove an inside cube is indeed a polyhedron. That this would pose a problem was noted with reference to Euler's formula $V-L+F=2$ for the surface of a polyhedron: Lhullier in a 1819 paper noticed that a cube inside a cube was not verifying the formula. Proofs of Euler's formula, at that time, where (usually implicitly) requiring convexity, though it is easy to produce examples of non convex polyhedra such that $V-L+F=2$. It took almost a century to switch point of view and realize that the complicated concept of polyhedron that many mathematicians were trying to understand was just a way to geometrically characterize the surface of polyhedra such that $V-L+F=2$ which is a cohomological condition.
This historical introduction just to state that it is possible that what you have in mind is that a solid surface should be a limited portion of space delimited by surfaces with the additional requirement of being cohomologically trivial.