Volume
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.
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