|
Volume (also called capacity) is a quantification of how much space an object occupies. The SI
unit for volume is the cubic 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.
The volume in acoustics refers to 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 4/3πr3.
Volume formulae
Common equations for volume:
- A cube: s3 (where s is the length of a side)
- A rectangular prism: l w h (length,
width, height)
- A cylinder: π r2 h (r = radius of circular face, h =
distance between faces)
- A sphere: 4 π r3 / 3 (r = radius of sphere)
- A cone: π r2 h / 3 (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 h (A = area of the base, h = height)
- any figure (calculus required): ∫ A dh (where h
is any dimension of the figure, and A 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: SI
A commonly used SI unit for volume is the liter, and one thousand liters is the volume of a cubic meter, which was
formerly termed a stere. A cubic centimeter is the same volume as a milliliter.
Volume measures: USA
Traditional US measures 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 pints, or about 946 ml
- US gallon = 128 ounces or four quarts, about 3.785 l
Volume measures: UK
Traditional UK measures 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 pints, or about 1.136 l
- UK gallon = 160 ounces or four 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 these pages:
See also: Orders of magnitude, mass, density
External links
|