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Volumes of Cones, Paraboloids, and Other "Vertex Solids"

by Paul B. Massell (United States Naval Academy)

This article originally appeared in:
Mathematics Magazine
April, 1991

Subject classification(s): Calculus | Several Variable Calculus | Multiple Integrals | Geometry and Topology | Solid Geometry | Cones
Applicable Course(s): 3.3 Mainstream Calculus III, IV | 4.9 Geometry

Using polar curves, the author defines "vertex solids", which include usual cones and paraboloids, and computes their volumes.

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Capsule Course Topic(s):
Multivariable Calculus | Double Integrals, Applications
Multivariable Calculus | Polar, Cylindrical and Spherical Coordinates
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