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Verify that the volume of the tetrahedron? practice calc exam help!?
Practice exam question that was given to us just kind of went over my head….i am so lost so if someone can explain how to do this that would be wonderful :)
Verify that the volume of the tetrahedron bounded by the plane: (x/a) + (y/b) + (z/c) = 1 in the first octant is (abc)/6; here a, b, and c are positive constants.
1 Answer
- Anonymous10 years agoFavorite Answer
The plane crosses the x-axis when y = z = 0 giving x = a.
Similarly it crosses the y-axis at y = b, and the z-axis at z = c.
If you regard the x, y plane as the base of the tetrahedron, it is a right triangle with legs of a, b so its area is ab/2.
The height will be z so volume = (1/3)*base area*height = (1/3)*(ab/2)*c = abc/6.