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.
Famous quotes containing the word volume:
“Measured by any standard known to scienceby horse-power, calories, volts, mass in any shape,the tension and vibration and volume and so-called progression of society were full a thousand times greater in 1900 than in 1800;Mthe force had doubled ten times over, and the speed, when measured by electrical standards as in telegraphy, approached infinity, and had annihilated both space and time. No law of material movement applied to it.”
—Henry Brooks Adams (18381918)
“I dare say I am compelled, unconsciously compelled, now to write volume after volume, as in past years I was compelled to go to sea, voyage after voyage. Leaves must follow upon each other as leagues used to follow in the days gone by, on and on to the appointed end, which, being Truth itself, is Oneone for all men and for all occupations.”
—Joseph Conrad (18571924)
“So it is with books, for the most part: they work no redemption on us. The bookseller might certainly know that his customers are in no respect better for the purchase and consumption of his wares. The volume is dear at a dollar, and after to reading to weariness the lettered backs, we leave the shop with a sigh, and learn, as I did without surprise of a surly bank director, that in bank parlors they estimate all stocks of this kind as rubbish.”
—Ralph Waldo Emerson (18031882)