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smc

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 ?
problem
(A)
(B)
(C)
(D)
Solution
It is a pyramid with height and base area , so using the formula for the volume of a pyramid, .
Final answer
A