FRUSTUM

Set of pyramidal frusta
Facesn trapezoids,
2 n-gon
Edges3n
Vertices2n
Symmetry group''C''''nv''
Dual polyhedron-
Propertiesconvex

A 'frustum' (plural: ''frusta'') is the portion of a solid – normally a cone or pyramid – which lies between two parallel planes cutting the solid. Degenerate cases are obtained for finite solids by cutting with a single plane only.

Contents
Pyramid Frustum
Examples
External links

Pyramid Frustum


Pyramidal frusta are a subclass of the prismatoids.
The formula for the volume of the frustum is
:V = rac{1}{3} h(B_1+sqrt{B_1 B_2}+B_2)
where ''h'' is the height from the top base to the bottom base, ''B1'' is the area of the bottom base, and ''B2'' is the area of the top base. (See also: Heronian mean.)
The formula for the volume of the cone frustum is
:V = rac{1}{3} pi h(R_1^2+R_1 R_2+R_2^2)
where п(pi)=3.141592654..., ''R1'' is the radius of the bottom base, and ''R2'' is the radius of the top base.
A more intuitive formula is: the volume of the cone (or other figure) before you sliced the top off, minus the volume of the cone (or other figure) that you sliced off:
:V = left | rac{1}{3} h_1 B_1 - rac{1}{3} h_2 B_2
ight |
The result comes from h = left | h_1 - h_2
ight | , and rac{B_1}{h_1^2}= rac{B_2}{h_2^2}.
Two frusta joined at their bases make a bifrustum.

Examples



★ An example of a pyramidal frustum may be seen on the reverse of the Great Seal of the United States, as on the back of the U.S. one-dollar bill. The "unfinished pyramid" is surmounted by the "Eye of Providence".

★ Certain ancient Native American mounds also form the frustum of a pyramid.

★ The John Hancock Center in Chicago, Illinois is a frustum whose bases are rectangles.

★ The Washington Monument is a narrow pyramidal frustum (with square bases) with a pyramid attached to the top base.

★ The focal field of a still or video camera forms a frustum. In 3D computer graphics, this is called the viewing frustum.

★ The spelling ''frust'r'um'', listed as "erroneous" by the Oxford English Dictionary, is frequently encountered and might be considered a variant. The Oxford English Dictionary gives both ''frusta'' and ''frustums'' for the plural.

External links



★

★

★ http://www.gomath.com/geometry/frustcone.php

This article provided by Wikipedia. To edit the contents of this article, click here for original source.

psst.. try this: add to faves
©2009 TripAtlas.com