Definition:Volume

Definition

Volume is the measure of the extent of a body.

It has three dimensions and is specified in units of length cubed.

Hence the term cube as a general vague term for a quantity in three dimensions.

It is a scalar quantity.

Symbol

The usual symbol used to denote the volume of a body is $V$.

Dimension

Volume is a dimension of measurement of physics.

The dimension of measurement of volume is:

$L^3$

length cubed.

Units

The SI unit of volume is the cubic metre:

$\mathrm m^3$

The CGS unit of volume is the cubic centimetre:

$\mathrm {cm}^3$

or, less formally:

$\mathrm {cc}$

Thus:

$1 \ \mathrm m^3 = 10^6 \ \mathrm {cm}^3 = 1 \,000 \,000 \ \mathrm {cc}$

Also known as

The term capacity can sometimes be seen in texts whose emphasis is on physics and applied mathematics.

In non-mathematical literature and popular puzzle pages, less precise terms can be seen, for example cubical contents.

Also see

• Results about volume can be found here.

Sources

• 1921: C.E. Weatherburn: Elementary Vector Analysis ... (previous) ... (next): Chapter $\text I$. Addition and Subtraction of Vectors. Centroids: Definitions: $1$. Scalar and vector quantities
• 1951: B. Hague: An Introduction to Vector Analysis (5th ed.) ... (previous) ... (next): Chapter $\text I$: Definitions. Elements of Vector Algebra: $1$. Scalar and Vector Quantities
• 1968: Murray R. Spiegel: Mathematical Handbook of Formulas and Tables ... (previous) ... (next): $\S 22$: Vectors and Scalars
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): dimension: 1.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): dimension: 1.
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): volume