A Sphere from a Max Volume

7/10Extremasolid geometry

Problem

Points A,B,CA, B, C lie on the surface of a sphere OO, with AOB=AOC=45\angle AOB = \angle AOC = 45^\circ. If the maximum possible volume of the tetrahedron O-ABCO\text{-}ABC is 23\dfrac{2}{3}, find the surface area of the sphere OO.

Answer

Solution

Difficulty7/10
TopicsExtrema, solid geometry

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