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2005 AMC 12A Question 17

AMC12 · 2005 AMC 12A

Question 17

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 $W?$

Question illustration
  1. $\dfrac{1}{12}$
  2. $\dfrac{1}{9}$
  3. $\dfrac{1}{8}$
  4. $\dfrac{1}{6}$
  5. $\dfrac{1}{4}$