# Dictionary Definition

cylindrical adj

2 related to or having the shape or properties of
a cylinder [syn: cylindric]

# User Contributed Dictionary

## English

### Adjective

- Shaped like a cylinder.

#### Translations

shaped like a cylinder

- Bulgarian: цилиндричен
- Czech: válcový, válcovitý
- Dutch: cylindervormig
- Finnish: liereä, lieriön muotoinen
- French: cylindrique
- German: zylindrisch
- Hungarian: hengeres
- Italian: cilindrico
- Russian: цилиндрический (tsilindríčeskij)
- Slovak: valcový, valcovitý

# Extensive Definition

A cylinder is one of the most basic curvilinear
geometric shapes: the surface formed by the points at
a fixed distance from a given straight
line, the axis of the cylinder. The solid enclosed by this
surface and by two planes perpendicular to the axis is also called
a cylinder. The surface area
and the volume of a
cylinder have been known since deep antiquity.

In differential
geometry, a cylinder is defined more broadly as any ruled
surface spanned by a one-parameter family of parallel lines.
The most common type of such generalized cylinders is given by
certain quadric
surfaces. A cylinder whose cross section is an ellipse, parabola, or hyperbola is called an
elliptic cylinder, parabolic cylinder, or hyperbolic
cylinder.

## Common usage

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 (height) h'', then its volume is given by

- V = \pi r^2 h \,

and its surface area
is:

- Area of the top is \pi r^2
- Area of the bottom is \pi r^2
- Area of the side is 2 \pi r h

Therefore without the top or bottom (lateral
area), the surface area is

- A = 2 \pi r h.

With the top and bottom, the surface area
is

- A = 2 \pi r^2 + 2 \pi r h = 2 \pi r ( r + h ).\,

For a given volume, the cylinder with the
smallest surface area has h = 2r. For a given surface area, the
cylinder with the largest volume has h = 2r, i.e. the cylinder fits
in a cube (height = diameter.)

## Other types of cylinders

An elliptic cylinder is a quadric
surface, with the following equation in Cartesian
coordinates:

- \left(\frac\right)^2 + \left(\frac\right)^2 = 1.

This equation is for an elliptic cylinder, a
generalization of the ordinary, circular cylinder (a = b). Even
more general is the generalized cylinder: the cross-section
can be any curve.

The cylinder is a degenerate quadric because at least one of
the coordinates (in this case z) does not appear in the
equation.

An oblique cylinder has the top and bottom
surfaces displaced from one another.

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

- \left(\frac\right)^2 + \left(\frac\right)^2 = -1

the hyperbolic cylinder:

- \left(\frac\right)^2 - \left(\frac\right)^2 = 1

and the parabolic cylinder:

- x^2 + 2ay = 0. \,

## Trivia

- The volume of the cylinder is 3 times the volume of a cone with equal radius.

## See also

- Steinmetz solid, the intersection of two or three perpendicular cylinders
- Prism (geometry)

## External links

- Surface area of a cylinder at MATHguide
- Volume of a cylinder at MATHguide
- Spinning Cylinder at Math Is Fun
- Volume of a cylinder Interactive animation at Math Open Reference

cylindrical in Arabic: أسطوانة (هندسة
رياضية)

cylindrical in Aymara: T'uyu

cylindrical in Azerbaijani: Silindr

cylindrical in Catalan: Cilindre

cylindrical in Czech: Válec

cylindrical in Danish: Cylinder (geometri)

cylindrical in German: Zylinder
(Geometrie)

cylindrical in Spanish: Cilindro

cylindrical in Esperanto: Cilindro

cylindrical in Basque: Zilindro

cylindrical in French: Cylindre

cylindrical in Korean: 원기둥

cylindrical in Ido: Cilindro

cylindrical in Indonesian: Silinder

cylindrical in Icelandic: Sívalningur

cylindrical in Italian: Cilindro
(geometria)

cylindrical in Hebrew: גליל (גאומטריה)

cylindrical in Lithuanian: Cilindras

cylindrical in Hungarian: Henger

cylindrical in Macedonian: Цилиндар
(геометрија)

cylindrical in Dutch: Cilinder

cylindrical in Japanese: 円柱 (数学)

cylindrical in Norwegian: Sylinder

cylindrical in Polish: Walec (bryła)

cylindrical in Portuguese: Cilindro

cylindrical in Romanian: Cilindru
(geometrie)

cylindrical in Quechua: Tiñiqi

cylindrical in Russian: Цилиндр

cylindrical in Albanian: Cilindri

cylindrical in Simple English: Cylinder

cylindrical in Slovenian: Valj

cylindrical in Serbian: Ваљак (геометрија)

cylindrical in Finnish: Lieriö

cylindrical in Swedish: Cylinder

cylindrical in Thai: ทรงกระบอก

cylindrical in Vietnamese: Hình trụ tròn

cylindrical in Turkish: Silindir

cylindrical in Ukrainian: Циліндр

cylindrical in Chinese: 圆柱体