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Volume of tetrahedron

  1. Mar 30, 2014 #1
    1. The problem statement, all variables and given/known data
    Set up an integral to find the volume of the tetrahedron with vertices
    (0,0,0), (2,1,0), (0,2,0), (0,0,3).


    2. Relevant equations



    3. The attempt at a solution
    My method of solving this involves using a triple integral. The first step is deciding on the bounds of the triple integral. If you can envision the tetrahedron in the x, y, z plane:

    The base of the tetrahedron has equations: y = x/2 and y = (4-x)/2

    I know the bounds for x and y:

    x goes from 0 to 2
    y goes from (x/2) to (4-x)/2

    How do I find the bounds for z? I need an equation relating z to x and y. . .
     
  2. jcsd
  3. Mar 30, 2014 #2
    Nevermind, I figured it out. I had to find the equation of the slanted plane by taking the cross product of two points getting the normal.

    Problem solved.
     
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