Frustum

Pronunciation: /ˈfrʌs təm/ Explain

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. Keller, Samuel Smith. Mathematics for Engineering Students, Plane and Solid Geometry. pg 166. www.archive.org. D. Van Nostrand Company. 1908. Last Accessed 8/6/2018. http://www.archive.org/stream/mathengineer00kellrich#page/166/mode/1up/search/apex. Buy the book
  2. Handbook of Formula and Physical Constants. www.archive.org. Power Engineering Training Systems. Last Accessed 8/6/2018. http://www.archive.org/stream/HandbookOfFormulaAndPhysicalConstants/HandbookOfFormulaeAndConstants#page/n11/mode/1up/search/frustum.

Cite this article as:

McAdams, David E. Frustum. 7/11/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/f/frustum.html.

Image Credits

Revision History

7/9/2018: Removed broken links, updated license, implemented new markup, implemented new Geogebra protocol. (McAdams, David E.)
2/5/2010: Added "References". (McAdams, David E.)
11/26/2008: Changed equations to images. (McAdams, David E.)
8/2/2008: Changed equations from images to Hot_Eqn. (McAdams, David E.)
7/6/2008: Corrected spelling. (McAdams, David E.)
6/6/2008: Initial version. (McAdams, David E.)

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