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Encyclopedia > Volume

The volume of a solid object is the three-dimensional concept of how much space it occupies, often quantified numerically. One-dimensional figures (such as lines) and two-dimensional shapes (such as squares) are assigned zero volume in the three-dimensional space. Look up volume in Wiktionary, the free dictionary. ... 2-dimensional renderings (ie. ... â€œLineâ€ redirects here. ... For other uses, see Square. ...

Volumes of straight-edged and circular shapes are calculated using arithmetic formulae. Volumes of other curved shapes are calculated using integral calculus, by approximating the given body with a large amount of small cubes or concentric cylindrical shells, and adding the individual volumes of those shapes. The volume of irregularly shaped objects can be determined by displacement. If an irregularly shaped object is less dense than the fluid, you will need a weight to attach to the floating object. A sufficient weight will cause the object to sink. The final volume of the unknown object can be found by subtracting the volume of the attached heavy object and the total fluid volume displaced. This article deals with the concept of an integral in calculus. ... Three dimensions A cube (or hexahedron) is a Platonic solid composed of six square faces, with three meeting at each vertex. ... A right circular cylinder An elliptic cylinder In mathematics, a cylinder is a quadric surface, with the following equation in Cartesian coordinates: This equation is for an elliptic cylinder, a generalization of the ordinary, circular cylinder (a = b). ... In fluid mechanics, displacement occurs when an object is immersed in a fluid, pushing it out of the way and taking its place. ...

The generalization of volume to arbitrarily many dimensions is called content.[citation needed] In differential geometry, volume is expressed by means of the volume form. Look up content in Wiktionary, the free dictionary. ... In mathematics, differential topology is the field dealing with differentiable functions on differentiable manifolds. ... In mathematics, a volume form is a nowhere zero differential n-form on an n-manifold. ...

Volume and Capacity are sometimes distinguished, with capacity being used for how much a container can hold (with contents measured commonly in litres or its derived units), and volume being how much space an object displaces (commonly measured in cubic metres or its derived units). The litre or liter (see spelling differences) is a unit of volume. ... The cubic meter (symbol mÂ³) is the SI derived unit of volume. ...

Volume and capacity are also distinguished in a capacity management setting, where capacity is defined as volume over a specified time period.

Volume is a fundamental parameter in thermodynamics and it is conjugate to pressure. Thermodynamics (from the Greek Î¸ÎµÏÎ¼Î·, therme, meaning heat and Î´Ï…Î½Î±Î¼Î¹Ï‚, dynamis, meaning power) is a branch of physics that studies the effects of changes in temperature, pressure, and volume on physical systems at the macroscopic scale by analyzing the collective motion of their particles using statistics. ... Thermodynamic potentials Maxwell relations Bridgmans equations Exact differential (edit) In thermodynamics, the internal energy of a system is expressed in terms of pairs of conjugate variables such as pressure/volume or temperature/entropy. ... This article is about pressure in the physical sciences. ...

Conjugate variables
of thermodynamics
Pressure Volume
(Stress) (Strain)
Temperature Entropy
Chem. potential Particle no.

## Volume formulas

Common equations for volume:
Shape Equation Variables
A cube: $s^3 = s cdot s cdot s$ s = length of a side
A rectangular prism: $l cdot w cdot h$ l = length, w = width, h = height
A cylinder (circular prism): $pi r^2 cdot h$ r = radius of circular face, h = height
Any prism that has a constant cross sectional area along the height**: $A cdot h$ A = area of the base, h = height
A sphere: $frac{4}{3} pi r^3$ r = radius of sphere
which is the integral of the Surface Area of a sphere
An ellipsoid: $frac{4}{3} pi abc$ a, b, c = semi-axes of ellipsoid
A pyramid: $frac{1}{3} lwh$ l = length, w = width, h = height
A cone (circular-based pyramid): $frac{1}{3} pi r^2 h$ r = radius of circle at base, h = distance from base to tip
Any figure (calculus required) $int A(h) ,dh$ h = any dimension of the figure, A(h) = area of the cross-sections perpendicular to h described as a function of the position along h
this will work for any figure if its cross-sectional area can be determined from h (no matter if the prism is slanted or the cross-sections change shape).

The volume of a parallelepiped is the absolute value of the scalar triple product of the subtending vectors, or equivalently the absolute value of the determinant of the corresponding matrix. In geometry, a parallelepiped (now usually pronounced , traditionally[1] in accordance with its etymology in Greek Ï€Î±ÏÎ±Î»Î»Î·Î»-ÎµÏ€Î¯Ï€ÎµÎ´Î¿Î½, a body having parallel planes) is a three-dimensional figure like a cube, except that its faces are not squares but parallelograms. ... In physics and engineering, a vector is a physical entity which has a magnitude which is a scalar (a physical quantity expressed as the product of a numerical value and a physical unit, not just a number). ... In algebra, a determinant is a function depending on n that associates a scalar, det(A), to every nÃ—n square matrix A. The fundamental geometric meaning of a determinant is as the scale factor for volume when A is regarded as a linear transformation. ...

The volume of any tetrahedron, given its vertices a, b, c and d, is (1/6)·|det(ab, bc, cd)|, or any other combination of pairs of vertices that form a simply connected graph. A tetrahedron (plural: tetrahedra) is a polyhedron composed of four triangular faces, three of which meet at each vertex. ... In algebra, a determinant is a function depending on n that associates a scalar, det(A), to every nÃ—n square matrix A. The fundamental geometric meaning of a determinant is as the scale factor for volume when A is regarded as a linear transformation. ...

## Volume measures: USA

U.S. customary units of volume: U.S. customary units, commonly known in the United States as English units or standard units, are units of measurement that are currently used in the U.S., in some cases alongside units from SI (the International System of Unitsâ€”the modern metric system). ...

• U.S. fluid ounce, about 29.6 mL
• U.S. liquid pint = 16 fluid ounces, or about 473 mL
• U.S. dry pint = 1/64 U.S. bushel, or about 551 mL (used for things such as blueberries)
• U.S. liquid quart = 32 fluid ounces, or about 946 mL
• U.S. dry quart = 1/32 U.S. bushel, or about 1.101 L
• U.S. liquid gallon = 128 fluid ounces or four U.S. quarts, about 3.785 L
• U.S. dry gallon = 1/8 U.S. bushel, or about 4.405 L
• U.S. (dry level) bushel = 2150.42 cubic inches, or about 35.239 L

The acre foot is often used in measuring the volume of water in a reservoir or 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 or exactly 1233.481 837 547 52 m³. The ounce (abbreviation: oz) is the name of a unit of mass in a number of different systems, including various systems of mass that form part of English units, Imperial units, and United States customary units. ... The pint is an English unit of volume or capacity in the imperial system and United States customary units, equivalent in each system to one half of a quart, and one eighth of a gallon. ... A table of weights from the secretaries of the different states, showing the no. ... For other uses, see Quart (disambiguation). ... The gallon (abbreviation: gal) is a unit of volume. ... The Ashokan Reservoir, located in Ulster County, New York, USA. It is one of 19 that supplies New York City with drinking water. ... An aquifer is an underground layer of water-bearing permeable rock or unconsolidated materials (gravel, sand, silt, or clay) from which groundwater can be usefully extracted using a water well. ... This article is about the physical quantity. ... An acre is the name of a unit of area in a number of different systems, including Imperial units and United States customary units. ... A foot (plural: feet or foot;[1] symbol or abbreviation: ft or, sometimes, â€² â€“ a prime) is a unit of length, in a number of different systems, including English units, Imperial units, and United States customary units. ...

A cubic inch is the volume of a cube which is one inch long on each edge. ... It has been suggested that Thousand Cubic Feet be merged into this article or section. ... The cubic yard (symbols ydÂ³, cu. ... A cubic mile is an Imperial unit/U.S. customary unit (non-SI non-metric) of volume, used in the United States. ...

## Volume measures: UK

The UK is undergoing metrication and is increasingly using the SI metric system's units of volume, i.e. cubic meter and litre. However, some former units of volume are still in varying degrees of usage: Metrication or metrification refers to the introduction of the SI metric system as the international standard for physical measurementsâ€”a long-term series of independent and systematic conversions from the various separate local systems of weights and measures. ... â€œSIâ€ redirects here. ... The cubic metre (symbol m³) is the SI derived unit of volume. ... The litre or liter (see spelling differences) is a unit of volume. ...

Imperial units of volume: The Imperial units are an irregularly standardized system of units that have been used in the United Kingdom and its former colonies, including the Commonwealth countries. ...

• UK fluid ounce, about 28.4 mL (this equals the volume of an avoirdupois ounce of water under certain conditions)
• UK pint = 20 fluid ounces, or about 568 mL
• UK quart = 40 ounces or two pints1.137 L
• UK gallon = 4 quarts, or exactly 4.546 09 L

The quart is now obsolete and the fluid ounce extremely rare. The gallon is only used for transportation uses, (it is illegal for petrol and diesel to be sold by the gallon). The pint is the only Imperial unit that is in everyday use, for the sale of draught beer and cider (bottled and canned beer is mainly sold in SI units) and for milk (this too is increasingly being sold in SI units, mainly Liters). The ounce (abbreviation: oz) is the name of a unit of mass in a number of different systems, including various systems of mass that form part of English units, Imperial units, and United States customary units. ... The pint is an English unit of volume or capacity in the imperial system and United States customary units, equivalent in each system to one half of a quart, and one eighth of a gallon. ... For other uses, see Quart (disambiguation). ... The gallon (abbreviation: gal) is a unit of volume. ...

## Volume measures: cooking

Traditional cooking measures for volume also include:

• teaspoon = 1/6 U.S. fluid ounce (about 4.929 mL)
• teaspoon = 1/6 Imperial fluid ounce (about 4.736 mL)
• teaspoon = 5 mL (metric)
• tablespoon = ½ U.S. fluid ounce or 3 teaspoons (about 14.79 mL)
• tablespoon = ½ Imperial fluid ounce or 3 teaspoons (about 14.21 mL)
• tablespoon = 15 mL or 3 teaspoons (metric)
• tablespoon = 5 fluidrams (about 17.76 mL) (British)
• cup = 8 U.S. fluid ounces or ½ U.S. liquid pint (about 237 mL)
• cup = 8 Imperial fluid ounces or ½ fluid pint (about 227 mL)
• cup = 250 mL (metric)

Image:Teaspoon sugar. ... This tablespoon has a capacity of about 1 tbsp. ... The dram (American spelling) or drachm (British spelling) is a small imperial unit of volume; it is also called the fluidram (contraction of fluid dram). ... The cup is a unit of measurement for volume, used in cooking to measure bulk foods, such as chopped vegetables (dry measurement), and liquids (fluid measurement). ...

## 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. In mathematics, two mathematical objects are considered equal if they are precisely the same in every way. ... For other uses, see Mass (disambiguation). ... In mathematics, especially in elementary arithmetic, division is an arithmetic operation which is the inverse of multiplication. ... In mathematics, an average or central tendency of a set (list) of data refers to a measure of the middle of the data set. ... For other uses, see Density (disambiguation). ...

The term specific volume is used for volume divided by mass. This is the reciprocal of the mass density, expressed in units such as cubic meters per kilogram (m³·kg-1). Specific volume is the volume of a unit of mass of a material. ... The reciprocal function: y = 1/x. ... Density (symbol: Ï - Greek: rho) is a measure of mass per unit of volume. ...

This article is about the physical quantity. ... Conversion of units refers to conversion factors between different units of measurement for the same quantity. ... For other uses, see Density (disambiguation). ... The pages linked in the right-hand column contain lists of volumes that are of the same order of magnitude (power of ten). ... For other uses, see Mass (disambiguation). ... For ton as a unit of mass, see ton The freight ton or measurement ton is a unit of volume used for describing ship capacities (tonnage) or cargo. ...

Results from FactBites:

 Volume Formulas (198 words) The volume of a figure is the number of cubes required to fill it completely, like blocks in a box. The volume of a rectangular prism is the length on the side times the width times the height. Volume is 1/3 feet times 1 foot times 3 feet = 1 cubic foot (or 1 cu.
 Volume Oscillator Confirms Price Movements (876 words) Volume, volume, volume – it is the indicator at which chartists constantly look to determine whether or not a move in the markets, a sector or a single issue has conviction. A volume oscillator measures volume by measuring the relationship between two moving averages. Volumes were low mostly because investors were still in shock; only the most steely-nerved investors got back in.
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