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Some SI units of volume to scale and approximate corresponding mass of water. To ease calculations, a unit of volume is equal to the volume occupied by a unit cube (with a side length of one). Because the volume occupies three dimensions, if the metre (m) is chosen as a unit of length, the corresponding unit of volume is the cubic metre (m 3).
Perimeter#Formulas – Path that surrounds an area; List of second moments of area; List of surface-area-to-volume ratios – Surface area per unit volume; List of surface area formulas – Measure of a two-dimensional surface; List of trigonometric identities; List of volume formulas – Quantity of three-dimensional space
For example, determining the volume of a sphere requires a significant amount of integral calculus or its geometrical analogue, the method of exhaustion. [3] However, having done this once in terms of some parameter (the radius for example), mathematicians have produced a formula to describe the volume of a sphere in terms of its radius:
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.
Specific volume: v: Volume per unit mass (reciprocal of density) m 3 ⋅kg −1: L 3 M −1: intensive Spin: S: Quantum-mechanically defined angular momentum of a particle kg⋅m 2 ⋅s −1: L 2 M T −1: Strain: ε: Extension per unit length unitless 1: Stress: σ: Force per unit oriented surface area Pa L −1 M T −2: order 2 tensor ...
More formulas of this nature can be given, as explained by Ramanujan's theory of elliptic functions to alternative bases. Perhaps the most notable hypergeometric inversions are the following two examples, involving the Ramanujan tau function τ {\displaystyle \tau } and the Fourier coefficients j {\displaystyle \mathrm {j} } of the J-invariant ...
This formula holds whether or not the cylinder is a right cylinder. [7] This formula may be established by using Cavalieri's principle. A solid elliptic right cylinder with the semi-axes a and b for the base ellipse and height h. In more generality, by the same principle, the volume of any cylinder is the product of the area of a base and the ...
Specific volume is commonly applied to: Molar volume; Volume (thermodynamics) Partial molar volume; Imagine a variable-volume, airtight chamber containing a certain number of atoms of oxygen gas. Consider the following four examples: If the chamber is made smaller without allowing gas in or out, the density increases and the specific volume ...
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