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  2. Frustum - Wikipedia

    en.wikipedia.org/wiki/Frustum

    The Egyptians knew the correct formula for the volume of such a truncated square pyramid, but no proof of this equation is given in the Moscow papyrus. The volume of a conical or pyramidal frustum is the volume of the solid before slicing its "apex" off, minus the volume of this "apex":

  3. Moscow Mathematical Papyrus - Wikipedia

    en.wikipedia.org/wiki/Moscow_Mathematical_Papyrus

    The fourteenth problem of the Moscow Mathematical calculates the volume of a frustum. Problem 14 states that a pyramid has been truncated in such a way that the top area is a square of length 2 units, the bottom a square of length 4 units, and the height 6 units, as shown. The volume is found to be 56 cubic units, which is correct. [1]

  4. Square pyramid - Wikipedia

    en.wikipedia.org/wiki/Square_pyramid

    Beyond the discovery of the volume of a square pyramid, the problem of finding the slope and height of a square pyramid can be found in the Rhind Mathematical Papyrus. [10] The Babylonian mathematicians also considered the volume of a frustum, but gave an incorrect formula for it. [11]

  5. Pyramid (geometry) - Wikipedia

    en.wikipedia.org/wiki/Pyramid_(geometry)

    Given that is the base's area and is the height of a pyramid, the volume of a pyramid is: [25] =. The volume of a pyramid was recorded back in ancient Egypt, where they calculated the volume of a square frustum, suggesting they acquainted the volume of a square pyramid. [26]

  6. Babylonian mathematics - Wikipedia

    en.wikipedia.org/wiki/Babylonian_mathematics

    The volume of a cylinder was taken as the product of the base and the height, however, the volume of the frustum of a cone or a square pyramid was incorrectly taken as the product of the height and half the sum of the bases. The Pythagorean rule was also known to the Babylonians. [19] [20] [21]

  7. Heronian mean - Wikipedia

    en.wikipedia.org/wiki/Heronian_mean

    The Heronian mean may be used in finding the volume of a frustum of a pyramid or cone. The volume is equal to the product of the height of the frustum and the Heronian mean of the areas of the opposing parallel faces. [2] A version of this formula, for square frusta, appears in the Moscow Mathematical Papyrus from Ancient Egyptian mathematics ...

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  9. Brahmagupta - Wikipedia

    en.wikipedia.org/wiki/Brahmagupta

    After giving the value of pi, he deals with the geometry of plane figures and solids, such as finding volumes and surface areas (or empty spaces dug out of solids). He finds the volume of rectangular prisms, pyramids, and the frustum of a square pyramid. He further finds the average depth of a series of pits.