A hypersphere is a higher-dimensional analogue of a sphere.
A hypersphere of radius r in n-dimensional Euclidean space consists of all points at distance r from a given fixed point (the centre of the hypersphere). This object is an (n-1)-manifold commonly called an (n-1)-sphere. Hence, the special case of an ordinary sphere in three dimensions would be called a "2-sphere".
The "volume" it encloses is
See also Hypercube 3-sphere