Volume

The term unit volume refers to the volume of one something: one quart, one milliliter, or one cubic inch, for example. Every measuring system that exists defines a unit volume for that system. Then, when one speaks about the volume of an object in that system, what he or she means is how many times that unit volume is contained within the object. If the volume of a glass of water is said to be 35.6 cubic inches, for example, what is meant is that 35.6 cubic inch unit volumes could be placed into that glass.

Mathematically, volume would seem to be a simple extension of the concept of area, but it is actually more complicated. The volume of simple figures with integral sides is found by determining the number of unit cubes that fit into the figure. When this idea is extended to include all possible positive real numbers, however, paradoxes of volume occur. It theoretically is possible to take a solid figure apart into a few pieces and reassemble it so that it has a different volume.

The units in which volume is measured depend on a variety of factors, such as the system of measurement being used and the type of material being measured. For example, volume in the British system of measurement may be measured in barrels, bushels, drams, gills, pecks, teaspoons, or other units. Each of these units may have more than one meaning, depending on the material being measured. For example, the precise size of a "barrel" ranges anywhere from 31 to 42 gallons, depending on federal and state statutes. The more standard units used in the British system, however, are the cubic inch or cubic foot and the gallon.

Variability in the basic units also exists. For example, the "quart" differs in size depending on whether it is being used to measure a liquid or dry volume and whether it is a measurement made in the British or customary U.S. system. As an example, 1 customary liquid quart is equivalent to 57.75 cubic inches, while 1 customary dry quart is equivalent to 67.201 cubic inches. In contrast, 1 British quart is equivalent to 69.354 cubic inches.

The basic unit of volume in the international system (often called the metric system) is the liter (abbreviated as l), although the cubic centimeter (cc or cm³) and milliliter (ml) are also widely used as units for measuring volume. The fundamental relationship between units in the two systems is given by the fact that 1 U.S. liquid quart is equivalent to 0.946 L or, conversely, 1 liter is equivalent to 1.057 customary liquid quarts.