Solid generated by the rotation of a circle *C* of radius *r* about an axis in the same plane at a distance *R* from its centre.

### Properties

The shape of a torus is determined by the two real parameters *R* and *r*:

- If R = 0, the corresponding torus is a sphere; in this case, it is also a
**solid torus** - If R < r, the corresponding torus is a self-intersecting
**spindle torus**, which resembles a pumpkin (the poles are flattened). - If R = r, the two poles coincide and it is a
**horn torus** - If R > r, the most common shape of the torus is obtained, that is, a
**ring torus**, which is shaped like a doughnut, as shown in the illustration above.

### Formulas

The volume *V* of a torus of radius *R* generated by a circle of radius *r* is given by:

*V* = 2\(π^{2}Rr^{2}\)

The area *A* of a torus of radius *R* generated by a circle of radius *r* is given by: *A* = 4\(π^{2}Rr\)