# Volume

## Etymology

Middle English, from Anglo-French, from Latin volumen roll, scroll, from volvere to roll

## Definitions

• 1 a : a series of printed sheets bound typically in book form : book
b : a series of issues of a periodical
c : album 1c
b : the amount of a substance occupying a particular volume
c : mass or the representation of mass in art or architecture

• Bulk

## Description

Volume is how much three-dimensional space a substance (solid, liquid, gas, or plasma) or shape occupies, 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.[1]