“Conical Frustum”的概念、定义、习题解题方法及翻译-数学辞典

单词

Conical Frustum

释义

Conical Frustum

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 top and bottom Radii.Then

(1)

The Surface Area, not including the top and bottom Circles, is

(2)

The Volume of the frustum is given by

(3)

But

(4)


			(5)

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

(6)

The weighted mean of

over the frustum is

(7)

The Centroid is then located at a height

(8)

(Beyer 1987, p. 133). The special case of the Cone is given by taking

,yielding

See also Cone, Frustum, Pyramidal Frustum, Spherical Segment

References

Beyer, W. H. (Ed.) CRC Standard Mathematical Tables, 28th ed. Boca Raton, FL: CRC Press, pp. 129-130 and 133, 1987.

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