Problem:
A unit cube is cut twice to form three triangular prisms, two of which are congruent, as shown in Figure . The cube is then cut in the same manner along the dashed lines shown in Figure . This creates nine pieces. What is the volume of the piece that contains vertex
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Figure 1 Figure 2
Answer Choices:
A.
B.
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E.
Solution:
The piece that contains is shown. It is a pyramid with vertices , and . Its base is a square with sides of length and its altitude is 1 . Hence the volume of this pyramid is
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The problems on this page are the property of the MAA's American Mathematics Competitions