Pyramidal Frustum


A pyramidal frustum is a frustum made by chopping the top off a pyramid. It is a special case of a prismatoid.

For a right pyramidal frustum, let s be the slant height, h the height, p_1 the bottom base perimeter, p_2 the top base perimeter, A_1 the bottom area, and A_2 the top area. Then the surface area (of the sides) and volume of a pyramidal frustum are given by


The geometric centroid of a right pyramidal frustum occurs at a height


above the bottom base (Harris and Stocker 1998).

The bases of a right n-gonal frustum are regular polygons of side lengths a and b with circumradii


where c is the side length, so the diagonal connecting corresponding vertices on top and bottom has length


and the edge length is


The triangular (n=3) and square (n=4) right pyramidal frustums therefore have side surface areas


The area of a regular n-gon is


so the volumes of these frustums are


See also

Conical Frustum, Frustum, Heronian Mean, Pyramid, Spherical Segment, Truncated Square Pyramid

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Beyer, W. H. (Ed.). CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 128, 1987.Dunham, W. Journey through Genius: The Great Theorems of Mathematics. New York: Wiley, pp. 3-4, 1990.Eves, H. A Survey of Geometry, rev. ed. Boston, MA: Allyn & Bacon, p. 7, 1965.Harris, J. W. and Stocker, H. "Frustum of a Pyramid." §4.3.2 in Handbook of Mathematics and Computational Science. New York: Springer-Verlag, p. 99, 1998.Kern, W. F. and Bland, J. R. "Frustum of Regular Pyramid." §28 in Solid Mensuration with Proofs, 2nd ed. New York: Wiley, pp. 67-71, 1948.

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Pyramidal Frustum

Cite this as:

Weisstein, Eric W. "Pyramidal Frustum." From MathWorld--A Wolfram Web Resource.

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