Mathematically, spheres are perfectly round two dimensional geometrical objects in three dimensional space. 

(from Greek σφαῖρα — sphaira, "globe, ball”) 

Like a circle, which geometrically is a two-dimensional object, a sphere is defined mathematically as the set of points that are all at the same distance r from a given point, but in three-dimensional space.

Surface area of a sphere


Spheres can only enclose volumes, because spheres are strictly 2 dimensional they have zero volume. But in 3 dimensions they can enclose a volume:


Source adapted from: Sphere. (2016, April 3). In Wikipedia, The Free Encyclopedia. Retrieved 07:31, May 2, 2016, from https://en.wikipedia.org/w/index.php?title=Sphere&oldid=713414917