Finding the volume of the tetrahedron with vertices (0,0,0), (2,0,0), (0,2,0), (0,0,2). I get 8; answer is 4/3.In this case, the tetrahedron is a parallelepiped object. If the bounds of such an object is given by the vectors A, B and C then the area of the object is A ⋅ ( B × C ). Let V be the volume we are trying to find. x 2 = 6 − y 2 − z 2 A = ( 2 , 0 , 0 ) − ( 0 , 0 , 0 ) = ( 2 , 0 , 0 ) B = ( 0 , 2 , 0 ) − ( 0 , 0 , 0 ) = ( 0 , 2 , 0 ) C = ( 0 , 0 , 2 ) − ( 0 , 0 , 0 ) = ( 0 , 0 , 2 ) V = | a 1 a 2 a 3 b 1 b 2 b 3 c 1 c 2 c 3 | = | 2 0 0 0 2 0 0 0 2 | = 2 | 2 0 0 2 | = 2 ( 4 − 0 ) = 8 However, the book gets 4 3

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Finding the volume of the tetrahedron with vertices (0,0,0), (2,0,0), (0,2,0), (0,0,2). I get 8; answer is 4/3.In this case, the tetrahedron is a parallelepiped object. If the bounds of such an object is given by the vectors A, B and C then the area of the object is   A  ⋅  (  B  ×  C  ). Let V be the volume we are trying to find.                              x          2                                    =        6        −                  y          2                −                  z          2                                    A                            =        (        2        ,        0        ,        0        )        −        (        0        ,        0        ,        0        )        =        (        2        ,        0        ,        0        )                            B                            =        (        0        ,        2        ,        0        )        −        (        0        ,        0        ,        0        )        =        (        0        ,        2        ,        0        )                            C                            =        (        0        ,        0        ,        2        )        −        (        0        ,        0        ,        0        )        =        (        0        ,        0        ,        2        )                            V                            =                  |                                                                      a                  1                                                                              a                  2                                                                              a                  3                                                                                                      b                  1                                                                              b                  2                                                                              b                  3                                                                                                      c                  1                                                                              c                  2                                                                              c                  3                                                              |                =                  |                                                    2                                            0                                            0                                                                    0                                            2                                            0                                                                    0                                            0                                            2                                              |                                                  =        2                  |                                                    2                                            0                                                                    0                                            2                                              |                =        2        (        4        −        0        )                                          =        8            However, the book gets       4    3

Kendrick Jacobs · Accepted Answer

Explanation:Note that the given volume is a cone with the height 2 and a right isosceles triangle of side 2 as the base. Thus, its volume can be calculated as       1    3    A  r  e      a          b      a      s      e        ⋅  H  e  i  g  h  t  =      1    3    (      1    2    ⋅  2  ⋅  2  )  2  =      4    3  .

Lorena Lester · Accepted Answer

Explanation:Your tetrahedron is also a pyramid. with the volume of       1    3    ⋅            2      ⋅      2        2    ⋅  2  =      4    3

Find the volume of the tetrahedron whose vertices are the given points: (0,0,0), (2,0,0), (0,2,0), (0,0,2).

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