## Paraboloid

The Surface of Revolution of the Parabola. It is a Quadratic Surface which can be specified by the Cartesian equation

 (1)

or parametrically by
 (2) (3) (4)

where , , and is the height.

The Volume of the paraboloid is

 (5)

The weighted mean of over the paraboloid is
 (6)

The Centroid is then given by
 (7)

(Beyer 1987).

See also Elliptic Paraboloid, Hyperbolic Paraboloid, Parabola

References

Beyer, W. H. (Ed.) CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, p. 133, 1987.

Gray, A. The Paraboloid.'' §11.5 in Modern Differential Geometry of Curves and Surfaces. Boca Raton, FL: CRC Press, pp. 221-222, 1993.

© 1996-9 Eric W. Weisstein
1999-05-26