A cubic meter (m3) is the base unit of volume in the International System of Units (SI). 1 cubic meter is equal to the volume of a cube with edges that measure 1 meter each.
Since the volume of a cube is calculated as length × width × height, the volume of the cube is 1 m3. The above cube can be referred to as a unit cube, where the unit in this case is the meter. One way to visualize volume is through use of unit cubes. For example, there are 16 unit cubes in the figure below. Since each cube measures 1 m3, the volume of the object is 16 m3.
In this manner, the volume of an object can be estimated as the number of unit cubes that fit within the object. In the above example, since the rectangular prism can be broken down into whole numbers of unit cubes, its volume can be calculated exactly. In cases where this is not possible, volume can be estimated using a combination of whole and partial unit cubes. Also, there are numerous formulas (such as length × width × height) that can be used to measure the volumes of various shapes.
Units of volume
A cubic meter is the base unit of volume in SI. As the base unit of volume in the most widely used system of measurement in the world, cubic meters are particularly significant. Cubic meters may be used to reference things such as the amount of water a household uses a year, or the amount of cement necessary to build a sidewalk.
One of the key benefits of SI is the use of SI prefixes to express larger or smaller volumes as multiples or submultiples of a base unit (in this case cubic meters). For example, cubic centimeters can be used to express smaller volumes, while a cubic kilometer may be used to express much larger volumes. In contrast to units of measurement in the US customary system, the aforementioned units are related by powers of 10 indicated by the prefixes used. The prefix "centi-" indicates 10-2 while the "kilo-" prefix indicates 103. There are therefore 1000 meters in a kilometer and 100 centimeters in a meter. Volume involves cubic units, and this is reflected in the relationship between cubic meters, cubic centimeters, and cubic kilometers:
- 1 m3 = (102 cm)3 = 1,000,000 cm3
- (103 m)3 = 1,000,000,000 m3 = 1 km3
SI prefixes can be used with other SI derived units of volume, or units of volume accepted for use with SI. One such example is the liter (and consequently the milliliter). The liter is a widely used unit of volume that is not an SI unit, but is accepted for use with SI, which is why SI prefixes can be applied to the liter.
Although the US also uses cubic meters (as well as liters) for a variety of applications, it still also uses a number of US customary units, such as cubic feet, cubic inches, gallons, pints, and more. These units are not related by some power of 10. Rather, each is related by some specific factor that can be difficult to remember. Below are some relationships between cubic meters and some measures of volume in the US customary system.
- 1 cubic meter = 61,023.744 cubic inches
- 1 cubic meter = 35.315 cubic feet
- 1 cubic meter = 264.172 gallons
- 1 cubic meter = 2113.376 pints
- 1 cubic meter = 67,628.045 tablespoons
Since so many different units of volume are used, it is important to be able to convert between them.
A household that uses an average of 100 gallons of water per day uses 36,500 gallons of water per year. How much water is this in cubic meters?
There are 264.172 gallons in 1 cubic meter, so divide 36,500 by 264.172:
36,500 ÷ 264.172 = 138.168 m3