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.
Volume formulae
Common equations for volume:
- A cube:
<math>s^3 = s \cdot s \cdot s<math> (where s is the length of a side)
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- A rectangular prism:
<math>l \cdot w \cdot h<math> (length, width, height)
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- A cylinder:
<math>\pi \cdot r^2 h<math> (r = radius of circular face, h = distance between faces)
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- A sphere:
<math>\frac{4}{3} \pi r^3<math> (r = radius of sphere)
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- An ellipsoid:
<math>\frac{4}{3} \pi abc<math> (a, b, c = semi-axes of ellipsoid)
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- A cone:
<math>\frac{1}{3} \pi r^2 h<math> (r = radius of circle at base, h = distance from base to tip)
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- Any prism that has a constant cross sectional area along the height**:
<math>A \cdot h<math> (A = area of the base, h = height)
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- Any figure (calculus required):
<math>\int A(h) dh<math> (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
