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2016 AMC 12B Question 23

AMC12 · 2016 AMC 12B

Question 23

What is the volume of the region in three-dimensional space defined by the inequalities $|x|+|y|+|z|\le1$ and $|x|+|y|+|z-1|\le1?$
  1. $\dfrac16$
  2. $\dfrac13$
  3. $\dfrac12$
  4. $\dfrac23$
  5. $1$