document.write( "Question 199322: In a cube, 10\" on a side, a sphere of maximum radius is inscribed. What is the size (diameter) of the largest sphere that can be placed in the space remaining in any of the eight corners? \n" ); document.write( "
Algebra.Com's Answer #149779 by RAY100(1637)\"\" \"About 
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A rough sketch will greatly aid in solving this
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\n" ); document.write( "diagonal of the cube is dia ^2 = 3 * 10 ^2,,,,diagonal is 17.320
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\n" ); document.write( "the largest sphere in the box has a dia of 10,,,sides of the box
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\n" ); document.write( "alone the diagonal, the distance left between sphere (r=5) and corner(diag = 17.32)
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\n" ); document.write( "is (17.32 - 10 ) /2 = 3.6602.
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\n" ); document.write( "now comes the hard part, a sphere of that dia will not fit, it goes to corner.
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\n" ); document.write( "to calculate a sphere that touches the sides of the cube, remember that 3.6602 is
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\n" ); document.write( "also the diagonal of a small box, that would fit in corner, with a small sphere inside.
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\n" ); document.write( "if the diagonal of the box is 3.6602, but s^2 +s^2 +s^2 = diag^2,,,s= sqrt ( diag^2 /3)
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\n" ); document.write( "s = sqrt 3.6602^2 /3 = 2.11,,,the diameter of the sphere \n" ); document.write( "
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