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Printjmc
geometry senior
Problem
A unit cube is cut twice to form three triangular prisms, two of which are congruent, as shown in Figure 1. The cube is then cut in the same manner along the dashed lines shown in Figure 2. This creates nine pieces. What is the volume of the piece that contains vertex ?
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
Final answer
\frac{1}{12}