document.write( "Question 611580: Two vertices of a cube have coordinates A(5, 12, 12) and B(20, 28, 24). What is the smallest possible volume of the cube? \n" ); document.write( "
Algebra.Com's Answer #385045 by Edwin McCravy(20056)\"\" \"About 
You can put this solution on YOUR website!
A(5, 12, 12) and B(20, 28, 24).
\n" ); document.write( "
\r\n" );
document.write( "The cube will be smallest if AB is an edge rather than a diagonal.\r\n" );
document.write( "\r\n" );
document.write( "The distance from A to B is found by the distance formula in 3-dimensions:\r\n" );
document.write( "\r\n" );
document.write( "d =  \r\n" );
document.write( "\r\n" );
document.write( "d = \"sqrt%28%2820-5%29%5E2%2B%2828-12%29%5E2+%2B+%2824-12%29%5E2%29\"\r\n" );
document.write( "\r\n" );
document.write( "d = \"sqrt%28%2815%29%5E2%2B%2816%29%5E2+%2B+%2812%29%5E2%29\"\r\n" );
document.write( "\r\n" );
document.write( "d = \"sqrt%28225%2B256+%2B+144%29\"\r\n" );
document.write( "\r\n" );
document.write( "d = \"sqrt%28625%29\"\r\n" );
document.write( "\r\n" );
document.write( "d = 25\r\n" );
document.write( "\r\n" );
document.write( "So each edge of the cube will be 25, and the volume is\r\n" );
document.write( "given by the formula:\r\n" );
document.write( "\r\n" );
document.write( "V = E³ where E is the length of an edge, or\r\n" );
document.write( "\r\n" );
document.write( "V = (25)³ = 15625 cubic units.\r\n" );
document.write( "\r\n" );
document.write( "Edwin
\r
\n" ); document.write( "\n" ); document.write( " \n" ); document.write( "
\n" );