document.write( "Question 829895: Finding the Maximum Volume Rectangular Prism in a given Sphere \n" ); document.write( "

Algebra.Com's Answer #500191 by Alan3354(69443) $\"\"$ $\"About$

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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\n" ); document.write( "s = side length of cube
\n" ); document.write( "r = radius of sphere
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\n" ); document.write( "d^2 = 4r^2 = 3s^2
\n" ); document.write( " $\"s+=+sqrt%284r%5E2%2F3%29\"$
\n" ); document.write( " $\"Vol+=+s%5E3+=+sqrt%2864r%5E6%2F27%29+=+sqrt%28d%5E6%2F27%29\"$
\n" ); document.write( " $\"Vol+=+d%5E3%2Asqrt%283%29%2F9\"$
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\n" ); document.write( "Proving that the regular cube gives max volume takes more work.
\n" ); document.write( "email via the TY note if you need to see that.
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