Question 829895
It's a regular cube with the long diagonal = diameter of the sphere.
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s = side length of cube
r = radius of sphere
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d^2 = 4r^2 = 3s^2
{{{s = sqrt(4r^2/3)}}}
{{{Vol = s^3 = sqrt(64r^6/27) = sqrt(d^6/27)}}}
{{{Vol = d^3*sqrt(3)/9}}}
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Proving that the regular cube gives max volume takes more work.
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