![]() 287 – 212 BCE) devised approximate volume formula of several shapes used the method of exhaustion approach, meaning to derive solutions from previous known formulas from similar shapes. The formula were determined by prior mathematicians by using a primitive form of integration, by breaking the shapes into smaller and simpler pieces. The last three books of Euclid's Elements, written in around 300 BCE, detailed the exact formulas for calculating the volume of parallelepipeds, cones, pyramids, cylinders, and spheres. : 116 The Egyptians use their units of length (the cubit, palm, digit) to devise their units of volume, such as the volume cubit : 117 or deny : 396 (1 cubit × 1 cubit × 1 cubit), volume palm (1 cubit × 1 cubit × 1 palm), and volume digit (1 cubit × 1 cubit × 1 digit). : 403 In the Reisner Papyrus, ancient Egyptians have written concrete units of volume for grain and liquids, as well as a table of length, width, depth, and volume for blocks of material. These math problems have been written in the Moscow Mathematical Papyrus (c. : 8 The earliest evidence of volume calculation came from ancient Egypt and Mesopotamia as mathematical problems, approximating volume of simple shapes such as cuboids, cylinders, frustum and cones. The precision of volume measurements in the ancient period usually ranges between 10–50 mL (0.3–2 US fl oz 0.4–2 imp fl oz). ![]() History Ancient history Ħ volumetric measures from the mens ponderia in Pompeii, an ancient municipal institution for the control of weights and measures Zero-, one- and two-dimensional objects have no volume in fourth and higher dimensions, an analogous concept to the normal volume is the hypervolume. Volumes of more complicated shapes can be calculated with integral calculus if a formula exists for the shape's boundary. Some simple three-dimensional shapes can have their volume easily calculated using arithmetic formulas. ![]() In ancient times, volume is measured using similar-shaped natural containers and later on, standardized containers. The volume of a container is generally understood to be the capacity of the container i.e., the amount of fluid (gas or liquid) that the container could hold, rather than the amount of space the container itself displaces. The definition of length (cubed) is interrelated with volume. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch). Volume is a measure of three-dimensional space.
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