HMMT 2004 U33
- Guts
- Answer
A plane slices through a cube of volume 1 with a cross-section in the shape of a regular hexagon. This cube also has an inscribed sphere, whose intersection with is a circle. What is the area of the region inside the regular hexagon but outside the circle?
Dataset text NuminaMath olympiads. Quoted with source.
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(3 \sqrt{3}-\pi) / 4
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