A rectangular cube (cuboid) is cut as shown, so that the cut goes through vertices , , and , and the triangular pyramid is removed. What is volume of what remains of the cuboid, if , , and ?
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Let the vertex of the pyramid be H . The volume of the pyramid E F G H is given by:
V pyramid = 3 1 × base area × height = 3 1 × [ E F H ] × H G = 3 1 × 2 a b × c = 6 a b c
Then the volume of what remains is given by:
V remains = V cuboid − V pyramid = a b c − 6 a b c = 6 5 a b c ≈ 1 1 6 . 6 7