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Australian AMC 2022 - Senior Question 21

AMC AUSTRALIA · Australian AMC 2022 - Senior

Question 21

A cuboctahedron is a solid formed by joining the midpoints of the edges of a cube as shown. What is the volume of a cuboctahedron of side length 2?

Question illustration
  1. $\frac{10\sqrt2}3$
  2. $\frac{40\sqrt2}3$
  3. $8\sqrt2$
  4. $6\sqrt2+8\sqrt3$
  5. $8\sqrt2+\frac83\sqrt3$