document.write( "Question 1015275: If a cube has an edge equal to the diagonal of another cube. Find the ratio of their volumes \n" ); document.write( "
Algebra.Com's Answer #631643 by rothauserc(4718)\"\" \"About 
You can put this solution on YOUR website!
I assume your cube's diagonal is not a space diagonal
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\n" ); document.write( "let e1 be an edge of cube 1, then volume of cube 1 is e1^3
\n" ); document.write( "We know that e1 is the diagonal of cube 2, let e2 be an edge of cube
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\n" ); document.write( "now use the Pythagorean Theorem
\n" ); document.write( "e1^2 = e2^2 + e2^2
\n" ); document.write( "2e2^2 = e1^2
\n" ); document.write( "e2 = e1/sqrt(2)
\n" ); document.write( "volume of cube 2 is e1^3 / (sqrt(2))^3 = e1^3 / (2sqrt(2))
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\n" ); document.write( "the ratio(R) of their volumes is e1^3 / (e1^3 / (2sqrt(2)))
\n" ); document.write( "R = (e1^3 * 2sqrt(2)) / e1^3 = 2sqrt(2)
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\n" ); document.write( "The other tutor's solution uses the space diagonal, I did not use that since the problem stated \"diagonal\" only.
\n" ); document.write( "It should be clear that a cube has two types of diagonals, one is on a face and the other is inside - called a space diagonal.\r
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