In geometry, a frustum (Latin for 'morsel');[a] (pl.: frusta or frustums) is the portion of a solid (normally a pyramid or a cone) that lies between two parallel planes cutting the solid. In the case of a pyramid, the base faces are polygonal and the side faces are trapezoidal. A right frustum is a right pyramid or a right cone truncated perpendicularly to its axis; otherwise, it is an oblique frustum.
In a truncated cone or truncated pyramid, the truncation plane is not necessarily parallel to the cone's base, as in a frustum.
If all its edges are forced to become of the same length, then a frustum becomes a prism (possibly oblique or/and with irregular bases).
Set of pyramidal right n-gonal frustums
Examples: right pentagonal and square frustums (n = 5 and n = 4)
A frustum's axis is that of the original cone or pyramid. A frustum is circular if it has circular bases; it is right if the axis is perpendicular to both bases, and oblique otherwise.
The height of a frustum is the perpendicular distance between the planes of the two bases.
Cones and pyramids can be viewed as degenerate cases of frusta, where one of the cutting planes passes through the apex (so that the corresponding base reduces to a point). The pyramidal frusta are a subclass of prismatoids.
^The term frustum comes from Latinfrustum, meaning 'piece' or 'morsel". The English word is often misspelled as frustrum, a different Latin word cognate to the English word "frustrate". The confusion between these two words is very old: a warning about them can be found in the Appendix Probi, and the works of Plautus include a pun on them.
^Clark, John Spencer (1895). Teachers' Manual: Books I–VIII. For Prang's complete course in form-study and drawing, Books 7–8. Prang Educational Company. p. 49.
^Kern, William F.; Bland, James R. (1938). Solid Mensuration with Proofs. p. 67.
^Nahin, Paul. An Imaginary Tale: The story of √−1. Princeton University Press. 1998
^"Mathwords.com: Frustum". Retrieved 17 July 2011.
^Al-Sammarraie, Ahmed T.; Vafai, Kambiz (2017). "Heat transfer augmentation through convergence angles in a pipe". Numerical Heat Transfer, Part A: Applications. 72 (3): 197−214. Bibcode:2017NHTA...72..197A. doi:10.1080/10407782.2017.1372670. S2CID 125509773.
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Derivation of formula for the volume of frustums of pyramid and cone (Mathalino.com)