Editing Cylinder (section)

==Types==
The definitions and results in this section are taken from the 1913 text ''Plane and Solid Geometry'' by [[George A. Wentworth]] and David Eugene Smith {{harv|Wentworth|Smith|1913}}.

A ''{{dfn|cylindrical surface}}'' is a [[Surface (mathematics)|surface]] consisting of all the points on all the lines which are [[parallel lines|parallel]] to a given line and which pass through a fixed [[plane curve]] in a plane not parallel to the given line. Any line in this family of parallel lines is called an ''element'' of the cylindrical surface. From a [[kinematics]] point of view, given a plane curve, called the ''directrix'', a cylindrical surface is that surface traced out by a line, called the ''generatrix'', not in the plane of the directrix, moving parallel to itself and always passing through the directrix. Any particular position of the generatrix is an element of the cylindrical surface.
[[File:Cylinders.svg|thumb|200px|A right and an oblique circular cylinder]]
A [[Solid geometry|solid]] bounded by a cylindrical surface and two [[parallel planes]] is called a (solid) ''{{dfn|cylinder}}''. The line segments determined by an element of the cylindrical surface between the two parallel planes is called an ''element of the cylinder''. All the elements of a cylinder have equal lengths. The region bounded by the cylindrical surface in either of the parallel planes is called a ''{{dfn|base}}'' of the cylinder. The two bases of a cylinder are [[congruence (geometry)|congruent]] figures. If the elements of the cylinder are perpendicular to the planes containing the bases, the cylinder is a ''{{dfn|right cylinder}}'', otherwise it is called an ''{{dfn|oblique cylinder}}''. If the bases are [[Disk (mathematics)|disks]] (regions whose boundary is a [[Circle (mathematics)|circle]]) the cylinder is called a ''{{dfn|circular cylinder}}''. In some elementary treatments, a cylinder always means a circular cylinder.<ref>{{citation |first=Harold R. |last=Jacobs |title=Geometry |year=1974 |publisher=W. H. Freeman and Co. |isbn=0-7167-0456-0 |page=607 }}</ref>
An ''{{dfn|open cylinder}}'' is a cylindrical surface without the bases.

The ''{{dfn|height}}'' (or altitude) of a cylinder is the [[perpendicular]] distance between its bases.

The cylinder obtained by rotating a [[line segment]] about a fixed line that it is parallel to is a ''{{dfn|cylinder of revolution}}''. A cylinder of revolution is a right circular cylinder. The height of a cylinder of revolution is the length of the generating line segment. The line that the segment is revolved about is called the ''{{dfn|axis}}'' of the cylinder and it passes through the centers of the two bases.
[[File:Circular cylinder rh.svg|thumb|180px|A right circular cylinder with radius {{math|''r''}} and height {{math|''h''}}]]

===Right circular cylinders===
{{main|Right circular cylinder}}
The bare term ''cylinder'' often refers to a solid cylinder with circular ends perpendicular to the axis, that is, a right circular cylinder, as shown in the figure. The cylindrical surface without the ends is called an ''{{dfn|open cylinder}}''. The formulae for the [[surface area]] and the [[volume]] of a right circular cylinder have been known from early antiquity.

A right circular cylinder can also be thought of as the [[solid of revolution]] generated by rotating a rectangle about one of its sides. These cylinders are used in an integration technique (the "disk method") for obtaining volumes of solids of revolution.{{sfn|Swokowski|1983|p=283}}

A tall and thin ''needle cylinder'' has a height much greater than its diameter, whereas a short and wide ''disk cylinder'' has a diameter much greater than its height.