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Volume is a measure of regions in three-dimensional space. [ 1] It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch ). The definition of length and height (cubed) is interrelated with volume.
In mathematics, a volume form or top-dimensional form is a differential form of degree equal to the differentiable manifold dimension. Thus on a manifold of dimension , a volume form is an -form. It is an element of the space of sections of the line bundle , denoted as . A manifold admits a nowhere-vanishing volume form if and only if it is ...
Molar volume. In chemistry and related fields, the molar volume, symbol Vm, [ 1] or of a substance is the ratio of the volume ( V) occupied by a substance to the amount of substance ( n ), usually at a given temperature and pressure. It is also equal to the molar mass ( M) divided by the mass density ( ρ ):
Specific volume is a property of materials, defined as the number of cubic meters occupied by one kilogram of a particular substance. The standard unit is the meter cubed per kilogram (m 3 /kg or m 3 ·kg −1 ). Sometimes specific volume is expressed in terms of the number of cubic centimeters occupied by one gram of a substance.
The surface-area-to-volume ratio or surface-to-volume ratio (denoted as SA:V, SA/V, or sa/vol) is the ratio between surface area and volume of an object or collection of objects. SA:V is an important concept in science and engineering. It is used to explain the relation between structure and function in processes occurring through the surface ...
This is a list of volume formulas of basic shapes: [4]: 405–406 Cone – 1 3 π r 2 h {\textstyle {\frac {1}{3}}\pi r^{2}h} , where r {\textstyle r} is the base 's radius Cube – a 3 {\textstyle a^{3}} , where a {\textstyle a} is the side's length;
Volume element. In mathematics, a volume element provides a means for integrating a function with respect to volume in various coordinate systems such as spherical coordinates and cylindrical coordinates. Thus a volume element is an expression of the form where the are the coordinates, so that the volume of any set can be computed by For ...
Unit of volume. A unit of volume is a unit of measurement for measuring volume or capacity, the extent of an object or space in three dimensions. Units of capacity may be used to specify the volume of fluids or bulk goods, for example water, rice, sugar, grain or flour.
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