Volume

Volume is the amount of space taken up by a particular object or material. There are many different methods for measuring volume, most of which vary based on the size, shape, or state of the object in question. Generally, volume is measured through mathematical equation or mechanical assessment. The calculation of volume has many practical purposes. Gases and liquids, for example, are often sold by volume.

Historical Background

Humankind's understanding of the concept of volume can be traced back to ancient times. Evidence exists that suggests that a number of different ancient civilizations, including the Sumerians, Egyptians, Greeks, and Chinese, all had some familiarity with the idea of volume and how to calculate it. Between about 250 B.C.E. and 100 B.C.E., the Greeks and Chinese developed some of the first written formulas for calculating the volume of spheres, cylinders, cubes, cuboids, and prisms.

The fundamental understanding of volume that arose in ancient times remained relatively unchanged until the mathematical field of calculus developed in the seventeenth century. This new branch of mathematics included an operation known as integration. Integration made it possible to calculate the area under any mathematically defined curve or any individual part of that curve. Eventually, scientists realized that integration could also be used to find volume under the right circumstances.

The last significant development in studying volume came with the advent of the computer. The immense computational power of computers made it possible to easily find the volume of any objects, even those with complex shapes that do not conform to the traditional mathematical equations for volume. Thanks to computers, finding volume has become a virtually effortless exercise.

Measuring Volume

Measuring volume is at once a simple and complicated matter. This is largely because the methods and units of measurement related to volume vary depending on the matter being measured. Because of these variations, finding volume can be as easy as completing a simple mathematical equation or difficult enough to require the assistance of advanced computers.

There is no single unit of measurement for volume. In most cases, the applicable unit of measurement for volume varies depending on the state of the object or substance in question. For solid objects, volume is usually measured in units of length, such as cubic inches, cubic meters, or cubic miles. The volume of liquids and gases, on the other hand, is typically measured in units like milliliters, liters, and quarts.

The methods of establishing a value for volume also vary according to the mass of the object or substance in question. The volume of regularly shaped solid objects is the easiest to find. In most cases, finding the volume of such an object simply requires a basic mathematical equation. For a simple rectangular box, it is only necessary to know the length, width, and height of the box to find its volume. In this case, volume can be determined with the equation volume = length ×width × height, or V = l × w × h. The volume of many other regularly shaped solid objects, like cubes, spheres, cones, and pyramids, can also be determined with similarly basic equations.

Not all solids have equations for volume, however. The volume of an irregularly shaped object can be determined in two main ways. One way is to subdivide the object in question into regular shapes, applying a standard volume equation to each, and then extrapolating the result to arrive at the object's total volume. The other way is to use a graduated cylinder to determine how much water the object displaces when submerged. Generally, the latter option is easier. To find the volume of an object in this manner, a graduated cylinder is filled with water to a recorded level. Once the object is submerged, the difference between the prerecorded water level and the level to which the water rises due to displacement is equal to the volume of the object.

Measuring the volume of liquids and gases requires entirely different methods. The volume of a liquid can be determined with virtually no effort at all because liquids naturally take the shape of the container in which they are placed. Finding liquid volume is as simple as placing the liquid in question in a container marked with some scale of measurement and recording the level to which the liquid rises.

Measuring the volume of gases may be far more difficult. Many gases are invisible to the naked eye and difficult to contain. In addition, the volume of a gas is heavily dependent on its temperature and pressure. Specifically, the volume of a gas is directly proportional to its temperature and inversely proportional to the amount of pressure under which it is held. This means that the volume of a gas is not constant. Therefore, in order to determine the volume of a given sample of gas, it is necessary to use a special device that clearly indicates the temperature and pressure of the gas.

Applications

Volume measurements have many practical uses. Many retailers sell liquid or gas goods, such as water or helium, by volume. Medical facilities often use volume to describe body-fat percentages, lung capacity, blood supply, and other health statistics. Many contractors use volume formulas to determine the amount of material they will need to complete particular tasks. Volume measurements are also important in preparing ingredients for recipes or adding cleaning solutions to water in swimming pools. Volume is an important factor in everyday life as well as in scientific study.

Bibliography

Lerner, K. Lee and Brenda Wilmoth Lerner, eds. "Volume." Real-Life Math. Vol. 2. Detroit: Gale, 2006, 575–82. Print.

McLaughlin, Charles William, PhD, Marilyn Thompson, PhD, and Dinah Zike. "Measuring Volume." Physical Science. Columbus, OH: Glencoe/McGraw-Hill, 2008, 18. Print.

Nagel, Rob, ed. "Volume." UXL Encyclopedia of Science. Vol. 10. Detroit: UXL, 2002, 1999–2002. Print.

Schlager, Neil, ed. "Density and Volume." Real-Life Physics. Vol. 2. Detroit: Gale, 2002, 21–26. Print.