Volume

The volume (Pl. volume or volumes, from the Latin volume " turn, bend ," from volvere " roll to roll " ), also: space or cubic content, is the solid content of a geometric body. Usual symbols is V.

In physics, refers to the volume expansion ( the footprint ) of a body. The (coherent ) SI unit for the unit of volume is the cubic meter ( unit symbol m3). Chance to read even the obsolete abbreviations cbm m³ and cc for cc. The liter unit is common to gases and liquids and as a 1 dm3 (10 × 10 × 10 cm ³), defined.

Technically, must be distinguished:

• Void volume of the free space within certain limits, such as the capacity of a container
• Volume, the volume of solid bodies, liquids or gases

History

The first known formulas for determining the volume (also stereometry ) originate from the early Egypt. The Moscow Papyrus is a collection of computing tasks and is dated to about 1850 BC. Among others, the formulas for determining the volumes of rectangular cones are described herein. The determination was achieved by analysis and subsequent synthesis. That is, the body is divided into several well-known body and the individual volumes are added.

Measurement methods

Over the years, many different methods for the determination of volumes have developed:

• Gauging: The body is filled with sand or water, whose amount is then determined in a known vessel; thus be in vessels, the volume of their interior determine.
• Displacement: The body is immersed in a completely water-filled vessel. The volume of the passing water is then (for example, cylinder), measured in a geometrically simple vessel. Due to the potential interactions between the sample body and the water can result in measurement errors, and therefore, other liquids can be used.
• For a body with a known density can be the volume also erwiegen.

Algebraic calculation

In theory, of known dimensions and shape of the body also the volume by calculation according to formulas valid for your body to be determined:

Examples:

• Cube with an edge length a:

• Parallelepiped with edge lengths a, b ​​and c:

• Sphere of radius r:

• Rotary body of the function f (x) upon rotation about the x -axis:

• Rotary body about the y axis:

• Body in sections orthogonal to the x axis: the body has a constant cross-section function with x in the interval (a, b) then, the volume:

• Cylinder or a prism with the base and the height h A:

• A cone or pyramid with the base A, and the height H:

• Any triangulated 3- dimensional object:

Generalization

One can define a volume via multi-dimensional manifolds, see also volume form. According to this generalization, the volume of a sub- space of the two-dimensional Euclidean space is equal to its surface area in three-dimensional Euclidean space and the same applies also in higher dimensional Euclidean spaces. For example, an n -dimensional hypercube with edge length a volume of.

The simplest polyhedral volume in n-dimensional space is the simplex which is defined by n 1 points. In three dimensions, a simplex is a tetrahedron, in two dimensions a triangle.

Cavity

A cavity is a mathematical, a physical or a natural object. A cavity having a volume that is referred to as void volume. A trapped in a tree volume can be a cavity. The existence of voids often, for example, with respect to strength or elasticity changed the surrounding structure (See porosity).

A natural cavity containing a vacuum or is filled with gas, liquids or other substances, which in turn may affect the surrounding structure. In particular, the interface between the cavity and structure may change, be difficult to detect or exist only at the conceptual level. A cavity having one or more openings, is thus not completely surrounded by the containing structure, is referred to colloquially as.

The size of the enclosed volume can often be calculated or determined experimentally. In some cases, this is however not possible in principle.

Cavitation is a frequently occurring phenomenon in geological and other physical and chemical processes.

Evacuated cavities have several universal properties, one of which is the black body radiation.

• Cavity as a vessel: bottle, tank, digestive system, sponge
• As ... Location: apartment, cave
• ... As a result of chemical or physical processes: bubble, soap bubble, "holes" in the cheese, blowholes