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General Prismatoid


A solid such that the area A_y of any section parallel to and a distance y from a fixed plane can be expressed as

 A_y=ay^3+by^2+cy+d.

The volume of such a solid is the same as for a prismatoid,

 V=1/6h(A_1+4M+A_2).

Examples include the cone, conical frustum, cylinder, prismatoid, pyramidal frustum, sphere, spherical segment, and spheroid.


See also

Prismatoid, Prismoid

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References

Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 132, 1987.Kern, W. F. and Bland, J. R. "The General Prismatoid." Ch. 8 in Solid Mensuration with Proofs, 2nd ed. New York: Wiley, pp. 120-130, 1948.

Referenced on Wolfram|Alpha

General Prismatoid

Cite this as:

Weisstein, Eric W. "General Prismatoid." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/GeneralPrismatoid.html

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