In a right circular cone, the semi-vertical angle of which is θ, a cube is placed so that four of its vertices are on the base and four on the curved surface. Prove that as θ varies the maximum of the ratio for the volume of the cube to the volume of the cone occurs when sin θ = 1/3.
Note: The semi-vertical angle of a cone is half the vertex angle.
For a cone with height h and radius r, tan θ = r/h.
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Posted by Liakms
on 2024-12-24 08:46:20 |
Good
