# Cylinder

## Three-dimensional solid / From Wikipedia, the free encyclopedia

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A **cylinder** (from Ancient Greek * *κύλινδρος* ( kúlindros)* 'roller, tumbler')

^{[1]}has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes. In elementary geometry, it is considered a prism with a circle as its base.

**Quick Facts**Type, Euler char. ...

Cylinder | |
---|---|

Type | Smooth surface Algebraic surface |

Euler char. | 2 |

Symmetry group | O(2)×O(1) |

Surface area | 2πr(r + h) |

Volume | πr^{2}h |

A cylinder may also be defined as an infinite curvilinear surface in various modern branches of geometry and topology. The shift in the basic meaning—solid versus surface (as in a solid ball versus sphere surface)—has created some ambiguity with terminology. The two concepts may be distinguished by referring to **solid cylinders** and **cylindrical surfaces**. In the literature the unadorned term cylinder could refer to either of these or to an even more specialized object, the *right circular cylinder*.