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,

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

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.