2 related to or having the shape or properties of a cylinder [syn: cylindric]
- Shaped like a cylinder.
shaped like a cylinder
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.
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
- \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. \,
- The volume of the cylinder is 3 times the volume of a cone with equal radius.
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