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. McAdams, David E.. All Math Words Dictionary, frustum. 2nd Classroom edition 20150108-4799968. pg 83. Life is a Story Problem LLC. January 8, 2015. Buy the book
  2. Keller, Samuel Smith. Mathematics for Engineering Students, Plane and Solid Geometry. pg 166. www.archive.org. D. Van Nostrand Company. 1908. Last Accessed 7/11/2018. http://www.archive.org/stream/mathengineer00kellrich#page/166/mode/1up/search/apex. Buy the book
  3. Handbook of Formula and Physical Constants. www.archive.org. Power Engineering Training Systems. Last Accessed 7/11/2018. http://www.archive.org/stream/HandbookOfFormulaAndPhysicalConstants/HandbookOfFormulaeAndConstants#page/n11/mode/1up/search/frustum.

Cite this article as:

McAdams, David E. Frustum. 12/21/2018. All Math Words Encyclopedia. Life is a Story Problem LLC. http://www.allmathwords.org/en/f/frustum.html.

Image Credits

Revision History

12/21/2018: Reviewed and corrected IPA pronunication. (McAdams, David E.)
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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