For geometrical problems involving spheres. Use the tag (geometry) as well. For intrinsic geometry of spheres, see (spherical-geometry).

An $n$-**sphere** is
$$ S^n = \{\mathbf x \in \mathbb{R}^{n+1}\mid \lVert x \rVert_2 = 1\}
$$
Its enclosed volume is the $(n+1)$-**ball**.