People have always been interested in comparing lengths, or how long one thing is to another. To compare, a unit length must be created. The first length known to be created was the cubit. The cubit was a unit of measure invented in ancient Egypt. The first ideas of volume follow the same concept only in three dimensions. An object could be measured by counting how many units an object was in length width and height and multiplying these to determine how many cube units could fit inside the object. In around 3000 BC, Egyptians use units of measurement to calculate volume of cubes and cuboids but quickly realized it was more difficult to calculate the volume of objects such as pyramids, spheres, and cylinders since it involved the idea of partial squared units. (Siegmund-Schultze, 2022) Thus, a mathematical search began.
Euclid’s elements, written around 300 BC, gave geometric formulas for calculating the volume of some shapes such as parallelepipeds, cones, pyramids, cylinders, and spheres. As well as in ancient Greece, scholars like Archimedes made significant contributions to the understanding of volume. Archimedes, in the 3rd century BC, laid the foundation for integral calculus to calculate the volume of a sphere (Eagle 1998) as well as other shells and unique globes and developed methods for calculating the volume of irregularly shaped objects, such as the famous Archimedes' principle, which relates the displacement of water to the volume of submerged objects (TedEd, 2021). Archimedes discovered this principle as he was taking a bath. He realized that the water level went up as he entered the bath. He then imagined that using this idea he could calculate the volume of an irregularly shaped object.
During the Middle Ages, the study of volume continued to evolve, with advancements in geometry and the understanding of solid geometry. Renaissance mathematicians like Kepler (Cardil, 2012) and Cavalieri made further progress in the development of integral calculus, which was crucial in calculating the volumes of more complex shapes.
The modern concept of volume as we know it today, based on the use of standard units and precise measurements, emerged with the creation of the metric system in the late 18th century and the development of scientific instrumentation for measuring volume more accurately. This system laid the foundation for the international standard units used in the measurement of volume today.
