Frustum

Pronunciation: /ˈfrʌs təm/ ?

A frustum is the part of a solid between two parallel planes.[1] Most often, frustum refers to a truncated cone or pyramid. The word frustum is often misspelled frustrum.

A frustum based on a cone is called a conical frustum. A frustum based on a pyramid is called a pyramidal frustum.

Right Conical Frustum

Conical frustum
Figure 1: Conical Frustum

Formulas for a right conical frustum:
R1 is the radius of the smaller circle.
R2 is the radius of the larger circle.
h is the height at the axis.
s is the slant height.
A is the surface area of the sides, not including the base and top.
V is the volume.

s=sqrt(R1-R1)^2+h^2
A=pi*(R1+R2)*s
V=(1/3)*pi*h*(R1^2+R1*R2+R2^2)

Right Pyramidal Frustum

Pyramidal frustum
Figure 1: Pyramidal Frustum

Formulas for a right pyramidal frustum:
p1 is the perimeter of the base.
p2 is the perimeter of the top.
h is the height.
s is the slant height.
A1 is the area of the base.
A2 is the area of the top.
S is the surface area not including the base or top.
V is the volume.

S=(1/2)*(p1+p2)*s
V=(1/3)h*(A1+sqrt(A1*a2)+A2)

References

  1. frustum. http://wordnet.princeton.edu/. WordNet. Princeton University. (Accessed: 2011-01-08). http://wordnetweb.princeton.edu/perl/webwn?s=frustum&sub=Search+WordNet&o2=&o0=1&o7=&o5=&o1=1&o6=&o4=&o3=&h=.
  2. Keller, Samuel Smith. Mathematics for Engineering Students, Plane and Solid Geometry, pg 166. D. Van Nostrand Company, 1908. (Accessed: 2010-01-02). http://www.archive.org/stream/mathengineer00kellrich#page/166/mode/1up/search/apex.
  3. Handbook of Formula and Physical Constants. Power Engineering Training Systems. (Accessed: 2010-02-05). http://www.archive.org/stream/HandbookOfFormulaAndPhysicalConstants/HandbookOfFormulaeAndConstants#page/n11/mode/1up/search/frustum.

Cite this article as:


Frustum. 2009-12-31. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/f/frustum.html.

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Revision History


2010-02-05: Added "References" (McAdams, David.)
2008-11-26: Changed equations to images (McAdams, David.)
2008-08-02: Changed equations from images to Hot_Eqn (McAdams, David.)
2008-07-06: Corrected spelling (McAdams, David.)
2008-06-06: Initial version (McAdams, David.)

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