Cylinder

A right circular cylinder

A cylinder is one of the most basic curved geometric shapes, with the surface formed by the points at a fixed distance from a given line segment, known as the axis of the cylinder. The shape can be thought of as a circular prism. Both the surface and the solid shape created inside can be called a cylinder. The surface area and the volume of a cylinder have been known since ancient times.

In differential geometry, a cylinder is defined more broadly as any ruled surface which is spanned by a one-parameter family of parallel lines. A cylinder whose cross section is an ellipse, parabola, or hyperbola is called an elliptic cylinder, parabolic cylinder, or hyperbolic cylinder respectively.

Common use

In common use a cylinder is taken to mean a finite section of a right circular cylinder, i.e., the cylinder with the generating lines perpendicular to the bases, 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 = πr2h

and its surface area is:

  • the area of the top r2) +
  • the area of the bottom r2) +
  • the area of the side (rh).

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

A = 2πrh.

With the top and bottom, the surface area is:

A = 2πr2 + 2πrh = 2πr(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 Languages
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azərbaycanca: Silindr
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български: Цилиндър
català: Cilindre
čeština: Válec
chiShona: Humburumbira
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eesti: Silinder
English: Cylinder
español: Cilindro
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euskara: Zilindro
فارسی: استوانه
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galego: Cilindro
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Latina: Cylindrus
latviešu: Cilindrs
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magyar: Henger
Bahasa Melayu: Silinder (geometri)
မြန်မာဘာသာ: ဆလင်ဒါ
日本語: 円柱 (数学)
Nordfriisk: Krais-Tsülinder
norsk: Sylinder
norsk nynorsk: Sylinder i matematikk
олык марий: Цилиндр
ਪੰਜਾਬੀ: ਸਿਲੰਡਰ
پنجابی: سلنڈر
Piemontèis: Cilìnder
português: Cilindro
Runa Simi: Tiñiqi
русский: Цилиндр
Scots: Ceelinder
shqip: Cilindri
sicilianu: Cilindru
slovenčina: Valec (geometria)
slovenščina: Valj
Soomaaliga: Dhululubo
کوردی: لوولەک
српски / srpski: Ваљак (геометрија)
srpskohrvatski / српскохрватски: Valjak (geometrija)
suomi: Lieriö
svenska: Cylinder
татарча/tatarça: Цилиндр
тоҷикӣ: Силиндр
Türkçe: Silindir
українська: Циліндр
Tiếng Việt: Hình trụ tròn
粵語: 圓柱
中文: 圆柱体