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. 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.
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.
Read more about Volume: Units, Related Terms, Volume Formulas
Famous quotes containing the word volume:
“A tattered copy of Johnson’s large Dictionary was a great delight to me, on account of the specimens of English versifications which I found in the Introduction. I learned them as if they were so many poems. I used to keep this old volume close to my pillow; and I amused myself when I awoke in the morning by reciting its jingling contrasts of iambic and trochaic and dactylic metre, and thinking what a charming occupation it must be to “make up” verses.”
—Lucy Larcom (1824–1893)
“There is a note in the front of the volume saying that no public reading ... may be given without first getting the author’s permission. It ought to be made much more difficult to do than that.”
—Robert Benchley (1889–1945)
“The other 1000 are principally the ‘old Yankee stock,’ who have lost the town, politically, to the Portuguese; who deplore the influx of the ‘off-Cape furriners’; and to whom a volume of genealogy is a piece of escape literature.”
—For the State of Massachusetts, U.S. public relief program (1935-1943)