A small sphere is centered at a corner of a large cube. What proportion of the surface of the sphere is inside of the cube?
Answer the same question with the cube replaced with a regular octahedron.
(In reply to
Possible answer by Larry)
You can easily fit 6 octahedra with room to spare, so the answer must be less than 1/6.
https://www.desmos.com/3d/r4k3i1tjkn
If you think about it, an octahedron is "pointier" than a cube, so the answer is probably less than 1/8.
(incidentally, I agree with Charlie's answer, but my method is simpler.)
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Posted by Jer
on 2025-02-28 13:30:16 |
re: Possible answer
