Volumes

Volum e refers to the amount of space enclosed within a boundary in three dimensions. In mathematics and the physical sciences, volume is a scalar quantity that measures the capacity of a region and is expressed in cubic units, with the cubic meter (m^3) as the SI unit. Practical units include liters (L) and milliliters (mL), where 1 m^3 = 1000 L and 1 L = 1000 cm^3. Density is defined as mass per unit volume.

In geometry, common formulas give the volume of simple shapes: the cube and rectangular prism have volume V = l w h; the cube is a special case where l = w = h and V = a^3. The right circular cylinder has V = π r^2 h, the sphere V = 4/3 π r^3, and the cone V = 1/3 π r^2 h. Volumes can also be determined for irregular objects by water displacement or, in calculus, by integration when cross-sectional areas are known.

In computing and information technology, a volume refers to a storage resource managed by an operating system. This can be a partition, a physical disk, or a logical volume. In cloud and container environments, volumes provide persistent storage that can be mounted to one or more machines or containers and preserved across restarts; Docker volumes are a common example.

In everyday use, volume also denotes the perceived loudness of sound, measured by amplitude, as well as a division of a publication or a book (a separate volume of a work).