Volume

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 squares) 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.

Contents

Volume formulae

Common equations for volume:

A cube:
s^3 = s \cdot s \cdot s (where s is the length of a side)
 
A rectangular prism:
l \cdot w \cdot h (length, width, height)
 
A cylinder:
\pi \cdot r^2 h (r = radius of circular face, h = distance between faces)
 
A sphere:
\frac{4}{3} \pi r^3 (r = radius of sphere)
 
An ellipsoid:
\frac{4}{3} \pi abc (a, b, c = semi-axes of ellipsoid)
 
A pyramid:
\frac{1}{3} A h (A = area of base, h = height from base to apex)
 
A cone (circular-based pyramid):
\frac{1}{3} \pi r^2 h (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 \cdot h (A = area of the base, h = height)
 
Any figure (calculus required):
\int A(h) dh (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:

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)

See also

External links



ca:Volum da:Rumfang de:Lautstärke fr:Volume es:volumen ja:体積 simple:Volume sv:Volym fi:Tilavuus

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