# Volume

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Volume

The volume of any solid, plasma, vacuum or theoretical object is how much three-dimensional space it occupies, often quantified numerically. One-dimensional figures (such as lines) and two-dimensional shapes (such as squares) are assigned zero volume in the three-dimensional space.Volume is presented as ml or cm3.

Volumes of straight-edged and circular shapes are calculated using arithmetic formulae. Volumes of other curved shapes are calculated using integral calculus, by approximating the given body with a large amount of small cubes or concentric cylindrical shells, and adding the individual volumes of those shapes. The volume of irregularly shaped objects can be determined by displacement. If an irregularly shaped object is less dense than the fluid, you will need a weight to attach to the floating object. A sufficient weight will cause the object to sink. The final volume of the unknown object can be found by subtracting the volume of the attached heavy object and the total fluid volume displaced.

In differential geometry, volume is expressed by means of the volume form, and is an important global Riemannian invariant.

Volume and capacity are sometimes distinguished, with capacity being used for how much a container can hold (with contents measured commonly in liters or its derived units), and volume being how much space an object displaces (commonly measured in cubic metrics or its derived units). The volume of a dispersed gas is the capacity of its container. If more gas is added to a closed container, the container either expands (as in a balloon) or the pressure inside the container increases.

Volume and capacity are also distinguished in a capacity management setting, where capacity is defined as volume over a specified time period.

Volume is a fundamental parameter in thermodynamics and it is conjugate to pressure.

Volume formulas

(The units of volume depend on the units of length - if the lengths are in meters, the volume will be in cubic meters, etc)

The volume of a parallelepiped is the absolute value of the scalar triple product of the subtending vectors, or equivalently the absolute value of the determinant of the corresponding matrix.

The volume of any tetrahedron, given its vertices a, b, c and d, is (1/6)·|det(ab, bc, cd)|, or any other combination of pairs of vertices that form a simply connected graph.

Volume measures: cooking

Traditional cooking measures for volume also include:
*teaspoon = 1/6 U.S. fluid ounce (about 4.929 mL)
*teaspoon = 1/6 Imperial fluid ounce (about 4.736 mL)
*teaspoon = 5 mL (metric)
*tablespoon = ½ U.S. fluid ounce or 3 teaspoons (about 14.79 mL)
*tablespoon = ½ Imperial fluid ounce or 3 teaspoons (about 14.21 mL)
*tablespoon = 15 mL or 3 teaspoons (metric)
*tablespoon = 5 fluidrams (about 17.76 mL) (British)
*cup = 8 U.S. fluid ounces or ½ U.S. liquid pint (about 237 mL)
*cup = 8 Imperial fluid ounces or ½ fluid pint (about 227 mL)
*cup = 250 mL (metric)

Relationship to density

The density of an object is defined as mass per unit volume.

The term "specific volume" is used for volume divided by mass. This is the reciprocal of the mass density, expressed in units such as cubic meters per kilogram.(m³·kg-1).

Volume formula derivation

See also

*Area
*Conversion of units
*Density
*Orders of magnitude (volume)
*Length
*Mass
*Weight
*Dimensioning
*Dimensional weight

External links

* [http://www.phy.ilstu.edu/~mnorton/Geometry.txt FORTRAN code for finding volumes of various shapes]
* [http://www.pneumofore.com/support/tools Unit Converter Tool also for Volume]

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• volume — [ vɔlym ] n. m. • XIIIe; lat. volumen « feuilles manuscrites enroulées », rad. volvere « rouler » I ♦ 1 ♦ (1270) Réunion d un certain nombre de cahiers (notamment imprimés) brochés ou reliés ensemble. ⇒ 1. livre. La bibliothèque royale « s… …   Encyclopédie Universelle

• Volume ! — Volume ! La revue des musiques populaires Ex Copyright Volume ! (2001 2008) Pays   …   Wikipédia en Français

• Volume — Vol ume, n. [F., from L. volumen a roll of writing, a book, volume, from volvere, volutum, to roll. See {Voluble}.] 1. A roll; a scroll; a written document rolled up for keeping or for use, after the manner of the ancients. [Obs.] [1913 Webster]… …   The Collaborative International Dictionary of English

• volume — VOLUME. s. m. Livre relié. Ce livre fera un juste volume. un beau volume. gros volume. grand volume. il y a vingt volumes sur cette tablette. On appelle, Livre en grand volume, Un livre in folio. Et on appelle, Livres en petit volume, Les livres… …   Dictionnaire de l'Académie française

• Volume I — Studioalbum von Queensberry Veröffentlichung 2008 Label Starwatch Music Format …   Deutsch Wikipedia

• Volume 1 (I¨s) — Iori (également le nom d un personnage du manga) est le nom du volume 1 du manga I¨s. Résumé Séto est amoureux en secret de Iori, qui est dans le même lycée que lui et qui fait du théâtre. Suite à une ancienne histoire d amour (où il avait révélé …   Wikipédia en Français

• Volume 4 — mey refer to: *Black Sabbath Vol 4, Black Sabbath s fourth studio album from 1972 *Led Zeppelin IV (official name ), Led Zeppelin s fourth studio album (released November 8, 1971): sometime called Led Zeppelin Volume 4 *Volume 4 (Yu Gi Oh! Set),… …   Wikipedia

• Volume I — (Fabrizio De André) Volume I Album par Fabrizio De André Sortie  1967 Enregistrement 18 juillet 1964 25 juillet 1964 Durée 30 min 29 sec …   Wikipédia en Français

• Volume 1 — DVD de Mushroomhead Publicación 9 de agosto de 2005 Grabación 2001 2004 Género(s) Industrial Metal Duración …   Wikipedia Español

• Volume 2 — DVD de Mushroomhead Publicación 28 de octubre de 2008 Grabación 2006 2007 Género(s) Industrial Metal Duración …   Wikipedia Español

• volume — s. m. 1. Espaço ocupado por um corpo qualquer. 2. Extensão, grossura de um objeto. 3. Unidade material que reúne, sob uma mesma capa, um certo número de folhas formando um todo ou fazendo parte de um conjunto. (Pode ser constituído por um ou mais …   Dicionário da Língua Portuguesa

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