Compute the volume of a tetrahedron. (a) Illustrate the tetrahedron that has vertices at (0,0,0), (2,0,0), (0, 4, 0), (0,0, 6), in Cartesian coordinates. This tetrahedron sits inside a box with side lengths 2, 4 and 6. The volume of this box is V = 2 x 4 x 6 = 48 cubic units. The volume of the tetrahedron must be some fraction of this.

Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
Chapter9: Surfaces And Solids
Section9.3: Cylinders And Cones
Problem 26E
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(1) Compute the volume of a tetrahedron.
(a) Illustrate the tetrahedron that has vertices at
(0,0,0),
(2,0,0), (0,4, 0), (0,0,6),
in Cartesian coordinates. This tetrahedron sits inside a box with side lengths 2, 4
and 6. The volume of this box is V = 2 x 4 × 6 = 48 cubic units. The volume of the
tetrahedron must be some fraction of this.
Transcribed Image Text:(1) Compute the volume of a tetrahedron. (a) Illustrate the tetrahedron that has vertices at (0,0,0), (2,0,0), (0,4, 0), (0,0,6), in Cartesian coordinates. This tetrahedron sits inside a box with side lengths 2, 4 and 6. The volume of this box is V = 2 x 4 × 6 = 48 cubic units. The volume of the tetrahedron must be some fraction of this.
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