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Math Help - Volume of a solid given 5 planes

  1. #1
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    Volume of a solid given 5 planes

    I know that the volume of a pyramid is:
    1/3 * (area of base) * height

    And I've found the area of a tetrahedron before,

    But I have no idea how to find the area of a solid figure given five planes in the 3-D coordinate system.

    The planes given are:
    x + 2y - 2z = 2
    2x + y + 2z = 4
    x = 2
    x = 0
    z = 2

    Any help or push in the right direction would be greatly appreciated
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  2. #2
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    Quote Originally Posted by jsmith90210 View Post
    I know that the volume of a pyramid is:
    1/3 * (area of base) * height

    And I've found the area of a tetrahedron before,

    But I have no idea how to find the area of a solid figure given five planes in the 3-D coordinate system.

    The planes given are:
    x + 2y - 2z = 2
    2x + y + 2z = 4
    x = 2
    x = 0
    z = 2

    Any help or push in the right direction would be greatly appreciated
    Start by drawing a picture. Since I have trouble drawing in 3 dimensions, I would start with just the xy-plane. x= 0 and x= 2 form the left and right boundaries. z= 2 is, of course, the "top".

    x+ 2y- 2z= 2 and 2x+ y+ 2z= 4, at z= 2, give x+ 2y- 4= 2 or x+ 2y= 6 and 2x+ y+ 4= 4 or 2x+ y= 0. Draw those line also in `the xy-plane to see where they intersect the lines x= 0 and x= 2.
    The planes x+ 2y- 2x= 2 and 2x+ y+ 2z= 4 intersect along the line 3x+ 3y= 6 or x+ y= 3.
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