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Math Help - Tetrahedron volume

  1. #1
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    Tetrahedron volume

    find volume of the tetrahedron bounded by the coordinate planes and the plane 2x+y+z=4

    how do i begin to find the limits of integration? This always seems to be the hardest part of these type of problems.
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  2. #2
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    Quote Originally Posted by cad2blender View Post
    find volume of the tetrahedron bounded by the coordinate planes and the plane 2x+y+z=4

    how do i begin to find the limits of integration? This always seems to be the hardest part of these type of problems.

    Intersection point with the z-axis: put x=y=0 and you get the point (0,0,4), with the y-axis put x=z=0 and get (0,4,0) and with the x-axis we get (2,0,0).
    Now you can use elementary geometry to calculate the volume \frac{(area\,\,of\,\,basis)\cdot height}{3} , or triple intgration: anyway, the volume is \frac{16}{3}, if I didn't make a mistake somewhere.

    Tonio
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  3. #3
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    so the limits of integration would be:

    for z 0 to -8x-y+16

    for y 0 to 4-2x

    for z 0 to 2

    I don't get the correct answer after using these limits
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