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The volume of a solid object is the three-dimensional concept of how much space it occupies, often quantified numerically. One-dimensional figures (such as line (mathematics)) and two-dimensional shapes (such as square (geometry)s) are assigned zero volume in the three-dimensional space.

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 cube (geometry) or concentric cylinder (geometry) shells, and adding the individual volumes of those shapes. The volume of irregularly shaped objects can be determined by Displacement (fluid). If an irregularly shaped object floats on water, you will need a heavier object like a rock or metal and attach it on you floating object. This should cause the object to sink. Then, get the volume of the object. Subtract the volume of the attached heavy object and the original findings.

The generalization of volume to arbitrarily many dimensions is called content. In differential geometry, volume is expressed by means of the volume form.

Volume and Capacity are sometimes distinguished, with capacity being used for how much a container can hold (with contents measured commonly in litres or its derived units), and volume being how much space an object displaces (commonly measured in cubic metres or its derived units).

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 variables (thermodynamics) to pressure.

Volume formulae {| class=prettytable|-! colspan = 3 | Common equations for volume:]:|s^3 = s \cdot s \cdot s|s = length of a side|-|A rectangular Prism (geometry):|l \cdot w \cdot h|l = length, w = width, h = height|-|A cylinder (geometry) (circular prism):|\pi r^2 \cdot h|r = radius of circular face, h = height|-|Any prism that has a constant cross sectional area along the height**:|A \cdot h|A = area of the base, h = height|-|A sphere:] of the Surface Area of a sphere:|\frac{4}{3} \pi abc|a, b, c = semi-axes of ellipsoid|-|A [Pyramid (geometry):|\frac{1}{3} lwh|l = length, w = width, h = height|-|A Cone (geometry) (circular-based pyramid):|\frac{1}{3} \pi r^2 h|r = radius of circle at base, h = distance from base to tip] required)|\int A(h) \,dh|h = any dimension of the figure, A(h) = area of the cross-sections perpendicular to h described as a function of the position along h
this will work for any figure if its cross-sectional area can be determined from h (no matter if the prism is slanted or the cross-sections change shape).

|}

(The units of volume depend on the units of length - if the lengths are in metres, the volume will be in cubic metres, 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)·](a−b, b−c, c−d)|, or any other combination of pairs of vertices that form a simply connected graph theory.

Volume measures: USA U.S. customary units of volume:

U.S. fluid ounce, about 29.6 mL
U.S. liquid pint = 16 fluid ounces, or about 473 mL
U.S. dry pint = 1/64 U.S. bushel, or about 551 mL (used for things such as blueberries)
U.S. liquid quart = 32 fluid ounces, or about 946 mL
U.S. dry quart = 1/32 U.S. bushel, or about 1.101 L
U.S. liquid gallon = 128 fluid ounces or four U.S. quarts, about 3.785 L
U.S. dry gallon = 1/8 U.S. bushel, or about 4.405 L
U.S. (dry level) bushel = 2150.42 cubic inches, or about 35.239 L

The acre foot is often used in measuring the volume of water in a reservoir (water) or an aquifer. It is the volume of water that would cover an area of one acre to a depth of one foot (unit of length). It is equivalent to 43,560 cubic feet or exactly 1233.481 837 547 52 m³.

cubic inch = 16.387064 cm³
cubic foot = 1,728 in³ ≈ 28.317 dm³
cubic yard = 27 ft³ ≈ 0.7646 m³
cubic mile = 5,451,776,000 yd³ = 3,379,200 acre-feet ≈ 4.168 km³

Volume measures: UK The UK is undergoing metrication and is increasingly using the International System of Units units of volume, i.e. cubic meter and litre. However, some former units of volume are still in varying degrees of usage:

Imperial units of volume:

UK fluid ounce, about 28.4 mL (this equals the volume of an avoirdupois ounce of water under certain conditions)
UK pint = 20 fluid ounces, or about 568 mL
UK quart = 40 ounces or two pints1.137 L
UK gallon = 4 quarts, or exactly 4.546 09 L

The quart is now obsolete and the fluid ounce extremely rare. The gallon is only used for transportation uses, (it is illegal for petrol and diesel to be sold by the gallon). The pint is the only Imperial unit that is in everyday use, for the sale of draught beer and cider (bottled and canned beer is mainly sold in SI units) and for milk (this too is increasingly being sold in SI units, mainly Liters).

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 (unit) = 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 volume of an object is equality (mathematics) to its mass division (mathematics) by its average density. This is a rearrangement of the calculation of density as mass per unit volume.

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

See also

External links

FORTRAN code for finding volumes of various shapes

Volume - Partners in Marketing
Volume - Partners in Marketing

BBC - Education Scotland - Standard Grade Bitesize Revision - Maths I ...
BBC - Education Scotland - Standard Grade Bitesize Revision - Maths I, Area and Volume, Volume, Introduction. Standard Grade Bitesize is the easy to use online revision service for ...

BBC - Skillswise Volume
Factsheets on calculating volume ... Quiz : Try this quiz and test your skills at working out volumes.

Volume - Wikipedia, the free encyclopedia
The volume of any solid, liquid, or gas is how much three-dimensional space it occupies, often quantified numerically. One-dimensional figures (such as lines) and two-dimensional ...

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Planning Portal - Volume Calculator
General Public. Navigation. Building Work; Planning; Building Regulations; Local Information; Useful Tools. Antenna Guide; Householders Guide; LDF Guide; Volume Calculator; Fee ...

Planning Portal - Approved Document B - Volume 1
Summary. This is Volume 1 of the revised Approved Document B. Volume 1 and Volume 2 replace the previous 2000 edition.

Definition: volume from Online Medical Dictionary
The Online Medical Dictionary is a searchable dictionary of definitions from medicine, science and technology.

Volume - Victoria and Albert Museum
24 November 2006 - 28 January 2007 Admission free The V&A and PlayStation present Volume Created by United Visual Artists and one point six. A luminous interactive installation ...

Parcel Volume Calculator | Parcel2Go.com
Use our parcel volume calculator to calculate either UK or international chargable weight.