# Cylinder

In

mathematics a

**cylinder** is a

quadric, i.e. a three-dimensional surface, with the following equation in

Cartesian coordinates:

This equation is for an elliptic cylinder. If a = b then the surface is a

*circular cylinder*. The cylinder is a

*degenerate quadric* because at least one of the coordinates (in this case

*z*) does not appear in the equation. By some definitions the cylinder is not considered to be a quadric at all.

In common usage, a *cylinder* is taken to mean a finite section of a right circular cylinder with its ends closed to form two circular surfaces, as in the figure (right). If the cylinder has a radius *r* and length *h*, then its volume is given by

and its

surface area is

For a given volume, the cylinder with the smallest surface area has

*h* = 2

*r*. For a given surface area, the cylinder with the largest volume has

*h* = 2

*r*.

There are other more unusual types of cylinder. These are the *imaginary elliptic cylinder*:

the

*hyperbolic cylinder*:

and the

*parabolic cylinder*:

A

**cylinder** in an

engine is the space a

piston travels in. The piston is the same size as the two bases of the cylinder (the circular and flat surfaces). In the following drawing, which depicts a cross-section of a steam engine cylinder, the bottom sliding part is the piston, and the top sliding part is a valve that directs steam into the two ends of the cylinder alternately.

The

**cylinder** was also the dominant medium of

audio storage from the

1870s to the

1910s, and continued in limited use (such as the

dictaphone) through the mid

20th century. See:

phonograph cylinder.