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.

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Since I use the definition "the set of all points in space that are equidistant from a fixed point", then yes, the shell. –  Ｊ. Ｍ. Sep 28 '11 at 16:16

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.

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The solid is called a ball. –  lhf Sep 28 '11 at 15:57
@lhf: I'd just remembered to add that when you posted your comment :) –  Zev Chonoles Sep 28 '11 at 16:00
Sometimes the solid is also called a "disc". –  MartianInvader Sep 28 '11 at 16:39