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On 7 April 1795, the metric system was formally defined in French law using six units. Three of these are related to volume: the stère (1 m 3) for volume of firewood; the litre (1 dm 3) for volumes of liquid; and the gramme, for mass—defined as the mass of one cubic centimetre of water at the temperature of melting ice. [10]
6 volumetric measures from the mens ponderia in Pompeii, a municipal institution for the control of weights and measures (79 A. D.). A unit of volume is a unit of measurement for measuring volume or capacity, the extent of an object or space in three dimensions.
Consider the linear subspace of the n-dimensional Euclidean space R n that is spanned by a collection of linearly independent vectors , …,. To find the volume element of the subspace, it is useful to know the fact from linear algebra that the volume of the parallelepiped spanned by the is the square root of the determinant of the Gramian matrix of the : (), = ….
The British imperial system uses a stone of 14 lb, a long hundredweight of 112 lb and a long ton of 2,240 lb. The stone is not a measurement of weight used in the US. The US customary system uses the short hundredweight of 100 lb and short ton of 2,000 lb. Where these systems most notably differ is in their units of volume.
The International System of Units, internationally known by the abbreviation SI (from French Système international d'unités), is the modern form of the metric system and the world's most widely used system of measurement. It is the only system of measurement with official status in nearly every country in the world, employed in science ...
The surface-area-to-volume ratio has physical dimension inverse length (L −1) and is therefore expressed in units of inverse metre (m −1) or its prefixed unit multiples and submultiples. As an example, a cube with sides of length 1 cm will have a surface area of 6 cm 2 and a volume of 1 cm 3. The surface to volume ratio for this cube is thus
Several problems in the Moscow Mathematical Papyrus (problem 14) and in the Rhind Mathematical Papyrus (numbers 44, 45, 46) compute the volume of a rectangular granary. [10] [11] Problem 14 of the Moscow Mathematical Papyrus computes the volume of a truncated pyramid, also known as a frustum.
In general, it is also called n-dimensional volume, n-volume, hypervolume, or simply volume. [1] It is used throughout real analysis , in particular to define Lebesgue integration . Sets that can be assigned a Lebesgue measure are called Lebesgue-measurable ; the measure of the Lebesgue-measurable set A is here denoted by λ ( A ).