volume

American Heritage Dictionary:

vol·ume

(vŏl'yūm, -yəm) pronunciation

1. A collection of written or printed sheets bound together; a book.
2. One of the books of a work printed and bound in more than one book.
3. A series of issues of a periodical, usually covering one calendar year.
4. A unit of written material assembled together and cataloged in a library.
A roll of parchment; a scroll.
(Abbr. V)
1. The amount of space occupied by a three-dimensional object or region of space, expressed in cubic units.
2. The capacity of such a region or of a specified container, expressed in cubic units.
1. Amount; quantity: a low volume of business; a considerable volume of lumber.
2. A large amount. Often used in the plural: volumes of praise.
1. The amplitude or loudness of a sound.
2. A control, as on a radio, for adjusting amplitude or loudness.

[Middle English, from Old French, from Latin volūmen, roll of writing, from volvere, to roll.]

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volume

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Symbol V. The space occupied by a body or mass of fluid.

TechEncyclopedia:

volume

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A physical storage unit, such as a hard disk, floppy disk, disk cartridge, CD-ROM disc or reel of tape. See volume label and logical volume.

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Barron's Finance & Investment Dictionary:

volume

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total number of stock shares, bonds, or commodities futures contracts traded in a particular period. Volume figures are reported daily by exchanges, both for individual issues trading and for the total amount of trading executed on the exchange. Technical analysts place great emphasis on the amount of volume that occurs in the trading of a security or a commodity futures contract. A sharp rise in volume is believed to signify future sharp rises or falls in price, because it reflects increased investor interest in a security, commodity, or market.
See also technical analysis; turnover.

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Roget's Thesaurus:

volume

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noun

A printed and bound work: book, tome. See words.
An issue of printed material offered for sale or distribution: opus, publication, title, work. See words.
Great extent, amount, or dimension. amplitude, bulk, magnitude, mass, size. See big/small/amount.

Oxford Dictionary of Sports Science & Medicine:

volume

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1. Measure of the amount of space occupied by a body.

2. In weight training, the total number of times a weight was lifted (sets × repetitions). For example, if the session was three sets of 10 repetitions, the volume would be 30. Volume indicates the total work performed.

Columbia Encyclopedia:

volume

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volume, measure of solid content or capacity, usually expressed in units that are the cubes of linear units, such as cubic inches and cubic centimeters, or in units of dry and liquid measure, such as bushels, gallons, and liters. Volumes of complicated geometric forms are often calculated using integral calculus. See the table entitled Formulas for the Volumes of Some Common Solids.

Investopedia Financial Dictionary:

Volume

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The number of shares or contracts traded in a security or an entire market during a given period of time. It is simply the amount of shares that trade hands from sellers to buyers as a measure of activity. If a buyer of a stock purchases 100 shares from a seller, then the volume for that period increases by 100 shares based on that transaction.

Investopedia Says:
Volume is an important indicator in technical analysis as it is used to measure the worth of a market move. If the markets have made strong price move either up or down the perceived strength of that move depends on the volume for that period. The higher the volume during that price move the more significant the move.

Related Links:
Use this indicator to validate a change in price direction and moving averages. Volume Oscillator Confirms Price Movements
Without supportive volume a price movement has no conviction, so rely on the indicator that shows the trend in volume. Volume Rate Of Change
This straightforward histogram can help you analyze the buying and selling interest in a stock. Gauging Support And Resistance With Price By Volume
Discover what on-balance volume, accumulation/distribution and open interest can tell you about the market. Gauging The Market's Psychological State
Find out how volume, the Aroon indicator and Fibonacci numbers can improve your profits. 3 Technical Tools To Improve Your Trading

Electronics Dictionary:

volume

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Magnitude or power level of audio frequency. Measured in volume units (VU).

Word Tutor:

volume

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IN BRIEF: One of the books of a set. Also: The amount of space inside something. Also: The amplitude or loudness of a sound.

Publishing a volume of verse is like dropping a rose petal down the Grand Canyon and waiting for the echo. — Don Marquis (1878-1937).

LearnThatWord.com is a free vocabulary and spelling program where you only pay for results!

Dictionary of Cultural Literacy: Science:

volume

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In mathematics, the amount of space occupied by an object measured in three dimensions, expressed in cubic units. In physics, the loudness of a sound.

Saunders Veterinary Dictionary:

volume

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The space occupied by a substance or a three-dimensional region; the capacity of such a region or of a container.

closing v. (CV) — the volume of gas in the lungs in excess of the residual volume at the time when small airways in the dependent portions close during maximal exhalation. See also closing volume.
v. of distribution — the calculated body space available for distribution of a drug. Abbreviated V_d.
minute v. — the volume of air expelled from the lungs per minute.
v. overload — see heart failure.
packed-cell v. (PCV) — the volume of packed red cells in milliliters per 100 ml of centrifuged blood. See also packed cell volume.

Mosby's Dental Dictionary:

volume

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Measure of the quantity of space occupied by a substance, such as air.

Random House Word Menu:

categories related to 'volume'

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Random House Word Menu by Stephen Glazier

For a list of words related to volume, see:

Quantities, Relationships, and Operations - volume: cubic magnitude of three-dimensional figure
Publications - volume: one of two or more separate books constituting a complete set; any single book
Journalism - volume: year’s issues of periodical, esp. bound into single volume
Advertising - volume: dollar amount of billings or revenue
Sound Reproduction Technology - volume: degree of loudness or intensity of sound
Sound, Hearing, and Deafness - volume: degree of sound intensity or loudness

Rhymes:

volume

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See words rhyming with "volume."

Bradford's Crossword Solver's Dictionary:

volume

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See crossword solutions for the clue Volume.

Wikipedia on Answers.com:

Volume

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For other uses, see Volume (disambiguation).

A measuring cup can be used to measure volumes of liquids. This cup measures volume in units of cups, fluid ounces, and millilitres.

Volume is the quantity of three-dimensional space enclosed by some closed boundary, for example, the space that a substance (solid, liquid, gas, or plasma) or shape occupies or contains.^[1] Volume is often quantified numerically using the SI derived unit, the cubic metre. The volume of a container is generally understood to be the capacity of the container, i. e. the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces.

Three dimensional mathematical shapes are also assigned volumes. Volumes of some simple shapes, such as regular, straight-edged, and circular shapes can be easily calculated using arithmetic formulas. The volumes of more complicated shapes can be calculated by integral calculus if a formula exists for the shape's boundary. One-dimensional figures (such as lines) and two-dimensional shapes (such as squares) are assigned zero volume in the three-dimensional space.

The volume of a solid (whether regularly or irregularly shaped) can be determined by fluid displacement. Displacement of liquid can also be used to determine the volume of a gas. The combined volume of two substances is usually greater than the volume of one of the substances. However, sometimes one substance dissolves in the other and the combined volume is not additive.^[2]

In differential geometry, volume is expressed by means of the volume form, and is an important global Riemannian invariant. In thermodynamics, volume is a fundamental parameter, and is a conjugate variable to pressure.

Contents

1 Units
2 Related terms
3 Volume formulas
- 3.1 Ratio of volumes of a cone, sphere and cylinder of the same radius and height
4 Volume formula derivations
- 4.1 Sphere
- 4.2 Cone
5 See also
6 References
7 External links

Units

Volume measurements from the 1914 The New Student's Reference Work.
Approximate conversion to millilitres:^[3]

	Imperial	U.S. liquid	U.S. dry
Gill	142 ml	118 ml	138 ml
Pint	568 ml	473 ml	551 ml
Quart	1137 ml	946 ml	1101 ml
Gallon	4546 ml	3785 ml	4405 ml

Any unit of length gives a corresponding unit of volume, namely the volume of a cube whose side has the given length. For example, a cubic centimetre (cm³) would be the volume of a cube whose sides are one centimetre (1 cm) in length.

In the International System of Units (SI), the standard unit of volume is the cubic metre (m³). The metric system also includes the litre (L) as a unit of volume, where one litre is the volume of a 10-centimetre cube. Thus

1 litre = (10 cm)³ = 1000 cubic centimetres = 0.001 cubic metres,

1 cubic metre = 1000 litres.

Small amounts of liquid are often measured in millilitres, where

1 millilitre = 0.001 litres = 1 cubic centimetre.

Various other traditional units of volume are also in use, including the cubic inch, the cubic foot, the cubic mile, the teaspoon, the tablespoon, the fluid ounce, the fluid dram, the gill, the pint, the quart, the gallon, the minim, the barrel, the cord, the peck, the bushel, and the hogshead.

Related terms

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).

Volume and capacity are also distinguished in capacity management, where capacity is defined as volume over a specified time period. However in this context the term volume may be more loosely interpreted to mean quantity.

The density of an object is defined as mass per unit volume. The inverse of density is specific volume which is defined as volume divided by mass. Specific volume is a concept important in thermodynamics where the volume of a working fluid is often an important parameter of a system being studied.

The volumetric flow rate in fluid dynamics is the volume of fluid which passes through a given surface per unit time (for example cubic meters per second [m³ s^-1]).

Volume formulas

Shape	Volume formula	Variables
Cube	$a^3\;$	a = length of any side (or edge)
Cylinder	$\pi r^2 h\;$	r = radius of circular face, h = height
Prism	$B \cdot h$	B = area of the base, h = height
Rectangular prism	$l \cdot w \cdot h$	l = length, w = width, h = height
Sphere	$\frac{4}{3} \pi r^3$	r = radius of sphere which is the integral of the surface area of a sphere
Ellipsoid	$\frac{4}{3} \pi abc$	a, b, c = semi-axes of ellipsoid
Pyramid	$\frac{1}{3}Bh$	B = area of the base, h = height of pyramid
Cone	$\frac{1}{3} \pi r^2 h$	r = radius of circle at base, h = distance from base to tip
Tetrahedron^[4]	${\sqrt{2}\over12}a^3 \,$	edge length $a$
Parallelepiped	$a b c \sqrt{K}$ $\begin{align} K =& 1+2\cos(\alpha)\cos(\beta)\cos(\gamma) \\ & - \cos^2(\alpha)-\cos^2(\beta)-\cos^2(\gamma) \end{align}$	a, b, and c are the parallelepiped edge lengths, and α, β, and γ are the internal angles between the edges
Any volumetric sweep (calculus required)	$\int_a^b A(h) \,\mathrm{d}h$	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. a and b are the limits of integration for the volumetric sweep. (This will work for any figure if its cross-sectional area can be determined from h).
Any rotated figure (washer method) (calculus required)	$\pi \int_a^b \left({\left[R_O(x)\right]}^2 - {\left[R_I(x)\right]}^2\right) \mathrm{d}x$	$R O$ and $R I$ are functions expressing the outer and inner radii of the function, respectively.
Klein bottle	$0\;$	No volume—it has no inside.

Ratio of volumes of a cone, sphere and cylinder of the same radius and height

A cone, sphere and cylinder of radius r and height h

The above formulas can be used to show that the volumes of a cone, sphere and cylinder of the same radius and height are in the ratio 1 : 2 : 3, as follows.

Let the radius be r and the height be h (which is 2r for the sphere), then the volume of cone is

$\tfrac{1}{3} \pi r^2 h = \tfrac{1}{3} \pi r^2 (2r) = (\tfrac{2}{3} \pi r^3) \times 1,$

the volume of the sphere is

$\tfrac{4}{3} \pi r^3 = (\tfrac{2}{3} \pi r^3) \times 2,$

while the volume of the cylinder is

$\pi r^2 h = \pi r^2 (2r) = (\tfrac{2}{3} \pi r^3) \times 3.$

The discovery of the 2 : 3 ratio of the volumes of the sphere and cylinder is credited to Archimedes.^[5]

Volume formula derivations

Sphere

The volume of a sphere is the integral of infinitesimal circular slabs of thickness dx. The calculation for the volume of a sphere with center 0 and radius r is as follows.

The surface area of the circular slab is $π r 2$ .

The radius of the circular slabs, defined such that the x-axis cuts perpendicularly through them, is;

$y = \sqrt{r^2-x^2}$

$z = \sqrt{r^2-x^2}$

where y or z can be taken to represent the radius of a slab at a particular x value.

Using y as the slab radius, the volume of the sphere can be calculated as $\int_{-r}^r \pi y^2 \,dx = \int_{-r}^r \pi(r^2 - x^2) \,dx.$

Now $\int_{-r}^r \pi r^2\,dx - \int_{-r}^r \pi x^2\,dx = \pi (r^3 + r^3) - \frac{\pi}{3}(r^3 + r^3) = 2\pi r^3 - \frac{2\pi r^3}{3}.$

Combining yields gives $V = \frac{4}{3}\pi r^3.$

This formula can be derived more quickly using the formula for the sphere's surface area, which is $4π r 2$ . The volume of the sphere consists of layers of infinitesimal spherical slabs, and the sphere volume is equal to

$\int_0^r 4\pi u^2 \,du$ = $\frac{4}{3}\pi r^3.$

Cone

The cone is a type of pyramidal shape. The fundamental equation for pyramids, one-third times base times altitude, applies cones as well. But for an explanation using calculus:

The volume of a cone is the integral of infinitesimal circular slabs of thickness dx. The calculation for the volume of a cone of height h, whose base is centered at (0,0,0) with radius r, is as follows.

The radius of each circular slab is r if x = 0 and 0 if x = h, and varying linearly in between—that is, $r\frac{(h-x)}{h}.$

The surface area of the circular slab is then $\pi \left(r\frac{(h-x)}{h}\right)^2 = \pi r^2\frac{(h-x)^2}{h^2}.$

The volume of the cone can then be calculated as $\int_{0}^h \pi r^2\frac{(h-x)^2}{h^2} dx,$

and after extraction of the constants: $\frac{\pi r^2}{h^2} \int_{0}^h (h-x)^2 dx$

Integrating gives us $\frac{\pi r^2}{h^2}\left(\frac{h^3}{3}\right) = \frac{1}{3}\pi r^2 h.$

References

^ "Your Dictionary entry for "volume"". http://www.yourdictionary.com/volume. Retrieved 2010-05-01.
^ One litre of sugar (about 970 grams) can dissolve in 0.6 litres of hot water, producing a total volume of less than one litre. "Solubility". http://chemed.chem.purdue.edu/genchem/topicreview/bp/ch18/soluble.php. Retrieved 2010-05-01. "Up to 1800 grams of sucrose can dissolve in a liter of water."
^ "General Tables of Units of Measurement". NIST Weights and Measures Division. http://ts.nist.gov/WeightsAndMeasures/Publications/appxc.cfm#4e. Retrieved 2011-01-12.
^ Coxeter, H. S. M.: Regular Polytopes (Methuen and Co., 1948). Table I(i).
^ Rorres, Chris. "Tomb of Archimedes: Sources". Courant Institute of Mathematical Sciences. http://www.math.nyu.edu/~crorres/Archimedes/Tomb/Cicero.html. Retrieved 2007-01-02.

External links

The Wikibook Geometry has a page on the topic of

Perimeters, Areas, Volumes

The Wikibook Calculus has a page on the topic of

Volume

Volume calculator - Javascript automatic calculator.

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Translations:

Volume

Top

Dansk (Danish)
n. - bind, nummer i rækken, årgang, rumfang, volumen, mængde, omfang

Nederlands (Dutch)
volume, boekdeel, jaargang, geluidssterkte, inhoud, album (muziek), papierrol, hoeveelheid, slinger/kring van rook etc., grote hoeveelheid, in boekdelen/albums etc. uitgeven, in volume toenemen, in/over een grote hoeveelheid

Français (French)
n. - (Mes, Phys) volume, capacité, volume, tome, (Audio) volume, puissance

Deutsch (German)
n. - Band, Lautstärke, Volumen, Rauminhalt, Umfang

Ελληνική (Greek)
n. - τόμος, (φυσ.) όγκος, κυβισμός, (τεχνολ.) ένταση ήχου, (μτφ.) (σημαντική) ποσότητα ή όγκος, σωρός, (οικον.) όγκος χρηματιστηριακών συναλλαγών

Italiano (Italian)
volume

idioms:

speak volumes dirla lunga

Português (Portuguese)
n. - volume (m), livro (m), capacidade (f)

idioms:

speak volumes falar muito

Русский (Russian)
том, объем, емкость, сила, клуб, переплетать в том

idioms:

speak volumes говорить многозначительно, выразительно

Español (Spanish)
n. - volumen, tomo, edición, capacidad

Svenska (Swedish)
n. - volym, band, omfång, tonstyrka, massa

中文（简体）(Chinese (Simplified))
体积, 册, 大小

中文（繁體）(Chinese (Traditional))
n. - 體積, 冊, 大小

한국어 (Korean)
n. - (전집 등의) 한 권, 다량, 음량

日本語 (Japanese)
n. - 冊, 巻, 本, 音量, 体積, 量, 大量, 書物, かさ, 多量

العربيه (Arabic)
‏(الاسم) مجلد ( كتاب), حجم, سعه, مفتاح الصوت ( مذياع)‏

עברית (Hebrew)
n. - ‮כרך, ספר, כמות, נפח, תפוסה, תכולה, שפעה, רוב, עוצמת קול, כמות גדולה‬

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		Saunders Veterinary Dictionary. Saunders Comprehensive Veterinary Dictionary 3rd Edition. Copyright © 2007 by D.C. Blood, V.P. Studdert and C.C. Gay, Elsevier. All rights reserved. Read more
		Mosby's Dental Dictionary. Mosby's Dental Dictionary. Copyright © 2004 by Elsevier, Inc. All rights reserved. Read more
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