CSMC 2023 Part A - Question 6, CEMC UWaterloo

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Difficulty: 9

This problem is tagged with csmc, csmc23, highschool.

(Canadian Senior Mathematics Contest 2023, Part A, Question 5, CEMC - UWaterloo)

Cube $ABCDEF GH$ has edge length $6$, and has $P$ on $BG$ so that $BP = PG$. What is the volume of the three-dimensional region that lies inside both square-based pyramid $EFGHP$ and square-based pyramid $ABCDG$?

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