document.write( "Question 765021: Find the surface area of the largest cube that can be cut from the sphere that has a radius of 5.00 cm. \n" ); document.write( "

Algebra.Com's Answer #465913 by ankor@dixie-net.com(22740) $\"\"$ $\"About$

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Find the surface area of the largest cube that can be cut from the sphere that has a radius of 5.00 cm.
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\n" ); document.write( "The diagonals to opposite corners of a cube that can be enclosed in the sphere
\n" ); document.write( "is the diameter 10 cm
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\n" ); document.write( "Let s = the side of the cube
\n" ); document.write( "the diagonal of one side of the cube = $\"sqrt%282s%5E2%29\"$
\n" ); document.write( "the length of diagonals to opposite corners:
\n" ); document.write( "s^2 + ( $\"sqrt%282s%5E2%29\"$ )^2 = 10^2
\n" ); document.write( "s^2 + 2s^2 = 100
\n" ); document.write( "3s^2 = 100
\n" ); document.write( "s^2 = 100/3
\n" ); document.write( "That is also the area of one side of the cube, therefore
\n" ); document.write( " $\"6%28100%2F3%29\"$ = 200 is area of the enclosed cube
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