2016 AMC 12B Problem 23

Geometry Level 3

What is the volume of the region in three-dimensional space defined by the inequalities ∣ x ∣ + ∣ y ∣ + ∣ z ∣ ≤ 1 |x|+|y|+|z|\leq 1 and ∣ x ∣ + ∣ y ∣ + ∣ z − 1 ∣ ≤ 1 |x|+|y|+|z-1|\leq 1 ?

Check out the whole set: 2016 AMC 12B Problems .
1 2 \frac{1}{2} 1 1 3 \frac{1}{3} 1 6 \frac{1}{6} 2 3 \frac{2}{3}

William Pan by William Pan , 17, USA

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