A conical frustum is a frustum created by slicing the top off a cone (with the cut made parallel to the base).
For a right circular cone , let be the slant height and and the base and top radii . Then

(1)

The surface area , not including the top and bottom
circles , is

The volume of the frustum is given by

(4)

But

(5)

so

This formula can be generalized to any pyramid by letting be the base areas
of the top and bottom of the frustum. Then the volume
can be written as

(9)

The area-weighted integral of over the frustum is

so the geometric centroid is located along
the z -axis at a height

(Eshbach 1975, p. 453; Beyer 1987, p. 133; Harris and Stocker 1998, p. 105). The special case of the cone is given by taking , yielding .

See also Cone ,

Frustum ,

Pyramidal Frustum ,

Spherical
Segment
Explore with Wolfram|Alpha
References Beyer, W. H. (Ed.). CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, pp. 129-130
and 133, 1987. Eshbach, O. W. Handbook
of Engineering Fundamentals. New York: Wiley, 1975. Harris, J. W.
and Stocker, H. "Frustum of a Right Circular Cone." §4.7.2 in Handbook
of Mathematics and Computational Science. New York: Springer-Verlag, p. 105,
1998. Kern, W. F. and Bland, J. R. "Frustum of Right Circular
Cone." §29 in Solid
Mensuration with Proofs, 2nd ed. New York: Wiley, pp. 71-75, 1948.
Cite this as:
Weisstein, Eric W. "Conical Frustum."
From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/ConicalFrustum.html

Subject classifications