Volume Details, Meaning Volume Article and Explanation Guide

Volume Guide, Meaning , Facts, Information and Description

Volume (also called capacity) is a quantification of how much space an object occupies. The SI unit for volume is the cubic metre (American spelling meter).

The volume of a solid object is a numerical value given to describe the three-dimensional concept of how much space it occupies. One-dimensional objects (such as lines) and two-dimensional objects (such as squaress) are assigned zero volume in three-dimensional space.

Volume in acoustics is used as a synonym for loudness. It is a common term for the amplitude or the level of sound. See also: DB(A), Sone, phon

Less commonly, in mathematics, volume can refer to the amount of space an n-dimensional object fills up, for some n > 3. Volumes are defined by means of integral calculus, by the decomposition of complex sets into small '\volume elements'. Volume (Cx³) is the antiderivative of area (Cx²). More simply, for a perfect closed curve, which is the sphere in three dimensions, the volume is the simple integral of the surface area. Thus, the surface area of a sphere is 4πr², and the volume is (4/3)πr³.

Table of contents

1 Volume formulae
2 Volume measures: Other SI units
3 Volume measures: USA
4 Volume measures: UK
5 Volume measures: cooking
6 Relationship to density
7 Volume comparisons
8 See also
9 External links

Volume formulae

Common equations for volume:

A cube:
(where s is the length of a side)

A rectangular prism:
(length, width, height)

A cylinder:
(r = radius of circular face, h = distance between faces)

A sphere:
(r = radius of sphere)

An ellipsoid:
(a, b, c = semi-axes of ellipsoid)

A pyramid:
(A = area of base, h = height from base to apex)

A cone (circular-based pyramid):
(r = radius of circle at base, h = distance from base to tip)

Any prism that has a constant cross sectional area along the height**:
(A = area of the base, h = height)

Any figure (calculus required):
(where h is any dimension of the figure, and A(h) is the area of the cross-sections perpendicular to h described as a function of the position along h; this will work for any figure (no matter if the prism is slanted or the cross-sections change shape).

Volume measures: Other SI units

A commonly used SI unit for volume is the litre (American spelling liter), and one thousand litres is the volume of a cubic metre (American spelling meter), which was formerly termed a stere. A cubic centimetre (American spelling centimeter) is the same volume as a millilitre.

Volume measures: USA

US customary units of volume:

US fluid ounce, about 29.6 ml (this volume of water weighs one ounce)
US pint = 16 ounces, or about 473 ml (this volume of water weighs one pound)
US quart = 32 ounces or two US pints, or about 946 ml
US gallon = 128 ounces or four US quarts, about 3.785 l

The acre foot is often used in measuring the volume of water in an aquifer. It is the volume of water that would cover an area of one acre to a depth of one foot. It is equivalent to 43,560 cubic feet.

Volume measures: UK

Imperial units of volume:

UK fluid ounce, about 28.4 ml (weight of this volume of water is 28.3 g, or nearly one ounce, 28.4 g)
UK pint = 20 fluid ounces, or about 568 ml
UK quart = 40 ounces or two UK pints, or about 1.136 l
UK gallon = 160 ounces or four UK quarts, or about 4.546 l

Volume measures: cooking

Traditional cooking measures for volume also include:

teaspoon = 1/6 ounce
tablespoon = 1/2 ounce or 3 teaspoons
cup = 8 ounces or 1/2 pint

Relationship to density

The volume of an object is equal to its mass divided by its average density. This is a rearrangement of the calculation of density as mass per unit volume.

Volume comparisons

To help compare different volumes, see Orders of magnitude (volume)

External links

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