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Volume of a region

  1. Jun 29, 2008 #1
    Find the volume of this region: The tetrahedron in the first octant bounded by the coordinate planes and the plane passing through (1, 0, 0), (0, 2, 0), and (0, 0, 3).

    Looking at this problem I thought it just involved solving a fairly simple triple integral:

    ||| dz dy dx

    With these limits of integration:
    0 <= x <= 1
    0 <= y <= 2
    0 <= z <= 3

    I get the answer 6, but my textbook says the answer is 1. Is this a typo in the textbook or did I do something stupid?
  2. jcsd
  3. Jun 29, 2008 #2


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    Homework Helper

    What are the equations of the planes which make up the tetrahedron? What you have done appears to be calculating the volume of a cuboid in the first octant of dimensions 1x2x3. That's not the shape of a tetrahedron.
  4. Jun 30, 2008 #3
    Oh I see, I have to come up with the equations of the planes myself. that was stupid of me..thanks!
  5. Jun 30, 2008 #4


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    Staff Emeritus
    Science Advisor

    Using constants for limits of integration gives the volume of the rectangular solid 0 <= x <= 1, 0 <= y <= 2, 0 <= z <= 3.
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