Rasalhague
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Does the word cone more correctly refer to a surface (like the word sphere), or a solid (like the word ball); and if it refers to the surface, what would the solid be called?
Is a Cone Considered a Solid or a Surface?
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Hi Rasalhague! 
You could aask the same question about "sphere", or "square" …
when we refer to a sphere, do we mean the surface, or the volume?
In all cases, the same name is used for both.
(ok, "ball" is unambiguous, but most people say "sphere" anyway)
The context usually makes it clear which is intended.
In the case of "cone", it nearly always refers to the surface.
You could aask the same question about "sphere", or "square" …
when we refer to a sphere, do we mean the surface, or the volume?
In all cases, the same name is used for both.
(ok, "ball" is unambiguous, but most people say "sphere" anyway)
The context usually makes it clear which is intended.
In the case of "cone", it nearly always refers to the surface.
Rasalhague
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Thanks, tiny-tim, I guess I'll just have to live with ambiguity!