Abstract

THE VOLUME OF A RECTANGULAR FRUSTUM: AN ALTERNATIVE METHOD

Olagunju Samuel Olu, Ph.D

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This paper presents an improvement on an early presentations on volumes of Frustums, a useful tool in a construction outfit. As a follow-up to an earlier presentation that considered Square and Conical Frustums, this paper considers the Volumes of a Rectangular Frustum as related to a Square Frustum, noting how they could depend on each other for estimation. It was noted that earlier papers discussed how the Egyptians obtained the volume of the pyramid as one-third the height multiplied by the sum of the two different areas A1 (from a large pyramid) and A2 (a smaller pyramid), added to the square-root of the product of the two areas {i.e. }. It was also noted that the usual method of estimating the volume of such dissected solid figures was by first calculating the volume of the original big pyramidal container, chopping off the top part as needed, calculating the volume of the chopped-off pyramid, and then subtracting the chopped-off volume from the original big pyramid. Such cumbersome calculation having been reduced by Olagunju (2011), to obtain a proven formula for a Square Frustum as , and in furtherance to this, Olagunju (2016) showed that the volume of a square frustum could be estimated using the known volume of a conical frustum (and vice versa). This has now been extended to obtain the volume of a Rectangular Frustum as . Where Volume of Rectangular Frustum, D = Diagonal of the large Rectangular base, d = diagonal of the small Rectangular top, and h = the height of the Rectangular Frustum. Keywords: Volume, Pyramids, Frustum, Rectangular, Square, Diagonals.

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