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
re(2): Possible answer by Larry)
Since there are 4*pi steradians in a sphere and there are 1/9.24441273502668 sphere equivalents at each of the vertices of the octahedron, there are a total of 6*pi/9.24441273502668 steradians total in the octahedron.
The octahedron has fewer vertices than the cube and each vertex has fewer steradians, so assumption 1 was wrong.
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Posted by Charlie
on 2025-03-02 11:22:04 |
re(3): Possible answer
