info prev up next book cdrom email home

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

\begin{displaymath}
A_y=ay^3+by^2+cy+d.
\end{displaymath}

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

\begin{displaymath}
V={\textstyle{1\over 6}} h(A_1+4M+A_2).
\end{displaymath}

Examples include the Cone, Cylinder, Prismatoid, Sphere, and Spheroid.

See also Prismatoid, Prismoid


References

Beyer, W. H. CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 132, 1987.




© 1996-9 Eric W. Weisstein
1999-05-25