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# Volume

Volume is the quantity of three-dimensional space enclosed by a closed surface, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains. 

113 relations: Acre-foot, Additive map, Archimedes, Area, Arithmetic, Banach–Tarski paradox, Barrel (unit), Board foot, Bushel, Calculus, Capacity management, Centimetre, Circle, Cone, Conjugate variables (thermodynamics), Cord (unit), Cotangent bundle, Cube, Cubic centimetre, Cubic foot, Cubic inch, Cubic metre, Cubic mile, Cubic yard, Cuboid, Cylinder, Cylindrical coordinate system, Density, Density on a manifold, Determinant, Differentiable manifold, Differential form, Differential geometry, Dimensional weight, Dimensioning, Disk (mathematics), Displacement (fluid), Dram (unit), Ellipsoid, Fluid, Fluid dynamics, Fluid ounce, Formula, Function (mathematics), Gallon, Gas, Gill (unit), Harold Scott MacDonald Coxeter, Hogshead, Ideal gas, ... Expand index (63 more) »

## Acre-foot

The acre-foot is a unit of volume commonly used in the United States in reference to large-scale water resources, such as reservoirs, aqueducts, canals, sewer flow capacity, irrigation water, and river flows.

## Additive map

In algebra an additive map, Z-linear map or additive function is a function that preserves the addition operation: for every pair of elements and in the domain.

## Archimedes

Archimedes of Syracuse (Ἀρχιμήδης) was a Greek mathematician, physicist, engineer, inventor, and astronomer.

## Area

Area is the quantity that expresses the extent of a two-dimensional figure or shape, or planar lamina, in the plane.

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## Arithmetic

Arithmetic (from the Greek ἀριθμός arithmos, "number") is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them—addition, subtraction, multiplication and division.

## Banach–Tarski paradox

The Banach–Tarski paradox is a theorem in set-theoretic geometry, which states the following: Given a solid ball in 3‑dimensional space, there exists a decomposition of the ball into a finite number of disjoint subsets, which can then be put back together in a different way to yield two identical copies of the original ball.

## Barrel (unit)

A barrel is one of several units of volume applied in various contexts; there are dry barrels, fluid barrels (such as the UK beer barrel and US beer barrel), oil barrels and so on.

## Board foot

The board-foot is a unit of measure for the volume of lumber in the United States and Canada.

## Bushel

A bushel (abbreviation: bsh. or bu.) is an imperial and US customary unit of weight or mass based upon an earlier measure of dry capacity.

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## Calculus

Calculus (from Latin calculus, literally 'small pebble', used for counting and calculations, as on an abacus), is the mathematical study of continuous change, in the same way that geometry is the study of shape and algebra is the study of generalizations of arithmetic operations.

## Capacity management

Capacity management's primary goal is to ensure that information technology resources are right-sized to meet current and future business requirements in a cost-effective manner.

## Centimetre

A centimetre (international spelling as used by the International Bureau of Weights and Measures; symbol cm) or centimeter (American spelling) is a unit of length in the metric system, equal to one hundredth of a metre, centi being the SI prefix for a factor of.

## Circle

A circle is a simple closed shape.

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## Cone

A cone is a three-dimensional geometric shape that tapers smoothly from a flat base (frequently, though not necessarily, circular) to a point called the apex or vertex.

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## Conjugate variables (thermodynamics)

In thermodynamics, the internal energy of a system is expressed in terms of pairs of conjugate variables such as temperature and entropy or pressure and volume.

## Cord (unit)

The cord is a unit of measure of dry volume used to measure firewood and pulpwood in the United States and Canada.

## Cotangent bundle

In mathematics, especially differential geometry, the cotangent bundle of a smooth manifold is the vector bundle of all the cotangent spaces at every point in the manifold.

## Cube

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex.

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## Cubic centimetre

A cubic centimetre (or cubic centimeter in US English) (SI unit symbol: cm3; non-SI abbreviations: cc and ccm) is a commonly used unit of volume that extends the derived SI-unit cubic metre, and corresponds to the volume of a cube that measures 1 cm × 1 cm × 1 cm.

## Cubic foot

The cubic foot (symbol ft3) is an imperial and US customary (non-metric) unit of volume, used in the United States, and partially in Canada, and the United Kingdom.

## Cubic inch

The cubic inch (symbol in3) is a unit of measurement for volume in the Imperial units and United States customary units systems.

## Cubic metre

The cubic metre (in British English and international spelling as used by the International Bureau of Weights and Measures) or cubic meter (in American English) is the SI derived unit of volume.

## Cubic mile

A cubic mile (abbreviation: cu mi or mi3) is an imperial and US customary (non-SI non-metric) unit of volume, used in the United States, Canada and the United Kingdom.

## Cubic yard

A cubic yard (symbol yd3) is an Imperial / U.S. customary (non-SI non-metric) unit of volume, used in the United States, Canada, and the UK.

## Cuboid

In geometry, a cuboid is a convex polyhedron bounded by six quadrilateral faces, whose polyhedral graph is the same as that of a cube.

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## Cylinder

A cylinder (from Greek κύλινδρος – kulindros, "roller, tumbler"), has traditionally been a three-dimensional solid, one of the most basic of curvilinear geometric shapes.

## Cylindrical coordinate system

A cylindrical coordinate system is a three-dimensional coordinate system that specifies point positions by the distance from a chosen reference axis, the direction from the axis relative to a chosen reference direction, and the distance from a chosen reference plane perpendicular to the axis.

## Density

The density, or more precisely, the volumetric mass density, of a substance is its mass per unit volume.

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## Density on a manifold

In mathematics, and specifically differential geometry, a density is a spatially varying quantity on a differentiable manifold that can be integrated in an intrinsic manner.

## Determinant

In linear algebra, the determinant is a value that can be computed from the elements of a square matrix.

## Differentiable manifold

In mathematics, a differentiable manifold (also differential manifold) is a type of manifold that is locally similar enough to a linear space to allow one to do calculus.

## Differential form

In the mathematical fields of differential geometry and tensor calculus, differential forms are an approach to multivariable calculus that is independent of coordinates.

## Differential geometry

Differential geometry is a mathematical discipline that uses the techniques of differential calculus, integral calculus, linear algebra and multilinear algebra to study problems in geometry.

## Dimensional weight

Dimensional weight, also known as volumetric weight, is a pricing technique for commercial freight transport (including courier and postal services), which uses an estimated weight that is calculated from the length, width and height of a package.

## Dimensioning

Dimensioning is the process of measuring either the area or the volume that an object occupies.

## Disk (mathematics)

In geometry, a disk (also spelled disc).

## Displacement (fluid)

In fluid mechanics, displacement occurs when an object is immersed in a fluid, pushing it out of the way and taking its place.

## Dram (unit)

The dram (alternative British spelling drachm; apothecary symbol ʒ or ℨ; abbreviated dr) Earlier version first published in New English Dictionary, 1897.

## Ellipsoid

An ellipsoid is a surface that may be obtained from a sphere by deforming it by means of directional scalings, or more generally, of an affine transformation.

## Fluid

In physics, a fluid is a substance that continually deforms (flows) under an applied shear stress.

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## Fluid dynamics

In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids - liquids and gases.

## Fluid ounce

A fluid ounce (abbreviated fl oz, fl. oz. or oz. fl., old forms ℥, fl ℥, f℥, ƒ ℥) is a unit of volume (also called capacity) typically used for measuring liquids.

## Formula

In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a chemical formula.

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## Function (mathematics)

In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.

## Gallon

The gallon is a unit of measurement for fluid capacity in both the US customary units and the British imperial systems of measurement.

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## Gas

Gas is one of the four fundamental states of matter (the others being solid, liquid, and plasma).

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## Gill (unit)

The gill (pronounced) or teacup is a unit of measurement for volume equal to a quarter of a pint.

## Harold Scott MacDonald Coxeter

Harold Scott MacDonald "Donald" Coxeter, FRS, FRSC, (February 9, 1907 &ndash; March 31, 2003) was a British-born Canadian geometer.

## Hogshead

A hogshead (abbreviated "Hhd", plural "Hhds") is a large cask of liquid (or, less often, of a food commodity).

## Ideal gas

An ideal gas is a theoretical gas composed of many randomly moving point particles whose only interactions are perfectly elastic collisions.

## Ideal gas law

The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas.

## Integral

In mathematics, an integral assigns numbers to functions in a way that can describe displacement, area, volume, and other concepts that arise by combining infinitesimal data.

## Intensive and extensive properties

Physical properties of materials and systems can often be categorized as being either intensive or extensive quantities, according to how the property changes when the size (or extent) of the system changes.

## International System of Units

The International System of Units (SI, abbreviated from the French Système international (d'unités)) is the modern form of the metric system, and is the most widely used system of measurement.

## Invariant (mathematics)

In mathematics, an invariant is a property, held by a class of mathematical objects, which remains unchanged when transformations of a certain type are applied to the objects.

## Length

In geometric measurements, length is the most extended dimension of an object.

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## Line (geometry)

The notion of line or straight line was introduced by ancient mathematicians to represent straight objects (i.e., having no curvature) with negligible width and depth.

## Liquid

A liquid is a nearly incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure.

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## Litre

The litre (SI spelling) or liter (American spelling) (symbols L or l, sometimes abbreviated ltr) is an SI accepted metric system unit of volume equal to 1 cubic decimetre (dm3), 1,000 cubic centimetres (cm3) or 1/1,000 cubic metre. A cubic decimetre (or litre) occupies a volume of 10 cm&times;10 cm&times;10 cm (see figure) and is thus equal to one-thousandth of a cubic metre. The original French metric system used the litre as a base unit. The word litre is derived from an older French unit, the litron, whose name came from Greek — where it was a unit of weight, not volume — via Latin, and which equalled approximately 0.831 litres. The litre was also used in several subsequent versions of the metric system and is accepted for use with the SI,, p. 124. ("Days" and "hours" are examples of other non-SI units that SI accepts.) although not an SI unit — the SI unit of volume is the cubic metre (m3). The spelling used by the International Bureau of Weights and Measures is "litre", a spelling which is shared by almost all English-speaking countries. The spelling "liter" is predominantly used in American English. One litre of liquid water has a mass of almost exactly one kilogram, because the kilogram was originally defined in 1795 as the mass of one cubic decimetre of water at the temperature of melting ice. Subsequent redefinitions of the metre and kilogram mean that this relationship is no longer exact.

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## Local coordinates

Local coordinates are measurement indices into a local coordinate system or a local coordinate space.

## Manifold

In mathematics, a manifold is a topological space that locally resembles Euclidean space near each point.

## Mass

Mass is both a property of a physical body and a measure of its resistance to acceleration (a change in its state of motion) when a net force is applied.

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## Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

## Measure (mathematics)

In mathematical analysis, a measure on a set is a systematic way to assign a number to each suitable subset of that set, intuitively interpreted as its size.

## Metric system

The metric system is an internationally adopted decimal system of measurement.

## Metric tensor

In the mathematical field of differential geometry, a metric tensor is a type of function which takes as input a pair of tangent vectors and at a point of a surface (or higher dimensional differentiable manifold) and produces a real number scalar in a way that generalizes many of the familiar properties of the dot product of vectors in Euclidean space.

## Minim (unit)

The minim (abbreviated min, ♏&#65038;, or) is a unit of volume in both the imperial and US customary systems of measurement.

## Multiple integral

The multiple integral is a definite integral of a function of more than one real variable, for example, or.

## One-form

In linear algebra, a one-form on a vector space is the same as a linear functional on the space.

## Orders of magnitude (volume)

The table lists various objects and units by the order of magnitude of their volume.

## Orientation (vector space)

In mathematics, orientation is a geometric notion that in two dimensions allows one to say when a cycle goes around clockwise or counterclockwise, and in three dimensions when a figure is left-handed or right-handed.

## Oxford English Dictionary

The Oxford English Dictionary (OED) is the main historical dictionary of the English language, published by the Oxford University Press.

## Parallelepiped

In geometry, a parallelepiped is a three-dimensional figure formed by six parallelograms (the term rhomboid is also sometimes used with this meaning).

## Peck

A peck is an imperial and United States customary unit of dry volume, equivalent to 2 dry gallons or 8 dry quarts or 16 dry pints (9.09 (UK) or 8.81 (US) liters).

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## Perimeter

A perimeter is a path that surrounds a two-dimensional shape.

## Pint

The pint (symbol pt, sometimes abbreviated as "p") is a unit of volume or capacity in both the imperial and United States customary measurement systems.

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## Plasma (physics)

Plasma (Henry George Liddell, Robert Scott, A Greek English Lexicon, on Perseus) is one of the four fundamental states of matter, and was first described by chemist Irving Langmuir in the 1920s.

## Pressure

Pressure (symbol: p or P) is the force applied perpendicular to the surface of an object per unit area over which that force is distributed.

## Prism (geometry)

In geometry, a prism is a polyhedron comprising an n-sided polygonal base, a second base which is a translated copy (rigidly moved without rotation) of the first, and n other faces (necessarily all parallelograms) joining corresponding sides of the two bases.

## Pseudo-Riemannian manifold

In differential geometry, a pseudo-Riemannian manifold (also called a semi-Riemannian manifold) is a generalization of a Riemannian manifold in which the metric tensor need not be positive-definite, but need only be a non-degenerate bilinear form, which is a weaker condition.

## Pyramid (geometry)

In geometry, a pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex.

## Quantity

Quantity is a property that can exist as a multitude or magnitude.

## Quart

The quart (abbreviation qt.) is an English unit of volume equal to a quarter gallon.

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## Rectangle

In Euclidean plane geometry, a rectangle is a quadrilateral with four right angles.

## Regular Polytopes (book)

Regular Polytopes is a mathematical geometry book written by Canadian mathematician Harold Scott MacDonald Coxeter.

## Riemannian geometry

Riemannian geometry is the branch of differential geometry that studies Riemannian manifolds, smooth manifolds with a Riemannian metric, i.e. with an inner product on the tangent space at each point that varies smoothly from point to point.

## SI derived unit

SI derived units are units of measurement derived from the seven base units specified by the International System of Units (SI).

## Solid

Solid is one of the four fundamental states of matter (the others being liquid, gas, and plasma).

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## Specific volume

In thermodynamics, the specific volume of a substance is the ratio of the substance's volume to its mass.

## Sphere

A sphere (from Greek σφαῖρα — sphaira, "globe, ball") is a perfectly round geometrical object in three-dimensional space that is the surface of a completely round ball (viz., analogous to the circular objects in two dimensions, where a "circle" circumscribes its "disk").

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## Spherical coordinate system

In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the radial distance of that point from a fixed origin, its polar angle measured from a fixed zenith direction, and the azimuth angle of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane.

## Square

In geometry, a square is a regular quadrilateral, which means that it has four equal sides and four equal angles (90-degree angles, or (100-gradian angles or right angles). It can also be defined as a rectangle in which two adjacent sides have equal length. A square with vertices ABCD would be denoted.

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## Square pyramid

In geometry, a square pyramid is a pyramid having a square base.

## State function

In thermodynamics, a state function or function of state is a function defined for a system relating several state variables or state quantities that depends only on the current equilibrium state of the system, for example a gas, a liquid, a solid, crystal, or emulsion.

## Surface (topology)

In topology and differential geometry, a surface is a two-dimensional manifold, and, as such, may be an "abstract surface" not embedded in any Euclidean space.

## Surface area

The surface area of a solid object is a measure of the total area that the surface of the object occupies.

## Tablespoon

A tablespoon is a large spoon used for serving or eating.

## Teaspoon

A teaspoon is an item of cutlery, a measuring instrument, of approximately 5ml, or a unit of measurement of volume (usually abbreviated tsp.).

## Tetrahedron

In geometry, a tetrahedron (plural: tetrahedra or tetrahedrons), also known as a triangular pyramid, is a polyhedron composed of four triangular faces, six straight edges, and four vertex corners.

## Thermodynamic state

For thermodynamics, a thermodynamic state of a system is its condition at a specific time, that is fully identified by values of a suitable set of parameters known as state variables, state parameters or thermodynamic variables.

## Thermodynamic system

A thermodynamic system is the material and radiative content of a macroscopic volume in space, that can be adequately described by thermodynamic state variables such as temperature, entropy, internal energy, and pressure.

## Thermodynamic temperature

Thermodynamic temperature is the absolute measure of temperature and is one of the principal parameters of thermodynamics.

## Thermodynamics

Thermodynamics is the branch of physics concerned with heat and temperature and their relation to energy and work.

## Three-dimensional space

Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called parameters) are required to determine the position of an element (i.e., point).

## Torus

In geometry, a torus (plural tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.

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## Triangular prism

In geometry, a triangular prism is a three-sided prism; it is a polyhedron made of a triangular base, a translated copy, and 3 faces joining corresponding sides.

## Two-dimensional space

Two-dimensional space or bi-dimensional space is a geometric setting in which two values (called parameters) are required to determine the position of an element (i.e., point).

## Unit of length

A unit of length refers to any discrete, pre-established length or distance having a constant magnitude which is used as a reference or convention to express linear dimension.

## Volume (thermodynamics)

In thermodynamics, the volume of a system is an important extensive parameter for describing its thermodynamic state.

## Volume form

In mathematics, a volume form on a differentiable manifold is a top-dimensional form (i.e., a differential form of top degree).

## Volumetric flow rate

In physics and engineering, in particular fluid dynamics and hydrometry, the volumetric flow rate (also known as volume flow rate, rate of fluid flow or volume velocity) is the volume of fluid which passes per unit time; usually represented by the symbol (sometimes). The SI unit is m3/s (cubic metres per second).

## Volumography

Volumography is the science, art and practice of creating three-dimensional space images by analyzing light or other electromagnetic radiation captured on a camera and calculating the volumetric measurements of recorded objects and deducting their geometry.

## Weight

In science and engineering, the weight of an object is related to the amount of force acting on the object, either due to gravity or to a reaction force that holds it in place.

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## References

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