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:
“We are too civil to books. For a few golden sentences we will turn over and actually read a volume of four or five hundred pages.”
—Ralph Waldo Emerson (18031882)
“And all the great traditions of the Past
They saw reflected in the coming time.
And thus forever with reverted look
The mystic volume of the world they read,
Spelling it backward, like a Hebrew book,
Till life became a Legend of the Dead.”
—Henry Wadsworth Longfellow (18091882)
“Bishop Berkeley destroyed this world in one volume octavo; and nothing remained, after his time, but mind; which experienced a similar fate from the hand of Hume in 1737.”
—Sydney Smith (17711845)