SOLUTION: Finding the Maximum Volume Rectangular Prism in a given Sphere

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Question 829895: Finding the Maximum Volume Rectangular Prism in a given Sphere
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
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%284r%5E2%2F3%29
Vol+=+s%5E3+=+sqrt%2864r%5E6%2F27%29+=+sqrt%28d%5E6%2F27%29
Vol+=+d%5E3%2Asqrt%283%29%2F9
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Proving that the regular cube gives max volume takes more work.
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