document.write( "Question 24342: This word problem is kind of tough, I am trying to figure out how to do it so could you please help me figure it out? P.S- how do you find the volume of a cube?\r
\n" ); document.write( "\n" ); document.write( "Question:
\n" ); document.write( "The edge of one cube is 4cm longer that the edge of a second cube. The volumes of the cubes differ by 316 cm2. Fid the length of each cube.\r
\n" ); document.write( "
\n" ); document.write( "\n" ); document.write( "--Thank You For Your Help \n" ); document.write( "
Algebra.Com's Answer #12933 by AnlytcPhil(1806)\"\" \"About 
You can put this solution on YOUR website!
This word problem is kind of tough, I am trying to figure out how to do it so\r\n" );
document.write( "could you please help me figure it out? P.S- how do you find the volume of a\r\n" );
document.write( "cube? \r\n" );
document.write( "Question:\r\n" );
document.write( "The edge of one cube is 4cm longer that the edge of a second cube. The volumes\r\n" );
document.write( "of the cubes differ by 316 cm3. Fid the length of each cube.\r\n" );
document.write( "\r\n" );
document.write( "The formula for the volume of a cube is\r\n" );
document.write( "\r\n" );
document.write( "     Volume = (edge)3  \r\n" );
document.write( "\r\n" );
document.write( "That's why they call a number raised to the 3rd power the \"CUBE\" of the number,\r\n" );
document.write( "for that's how you find the volume of a CUBE, by CUBING an edge!!!  \r\n" );
document.write( "\r\n" );
document.write( "     Anyway, let each edge of the second smaller cube be x cm.\r\n" );
document.write( "\r\n" );
document.write( ">>...The edge of one cube is 4cm longer that the edge of a second cube...<<\r\n" );
document.write( "\r\n" );
document.write( "So each edge of the first (larger) cube is x+4 cm\r\n" );
document.write( "\r\n" );
document.write( "\r\n" );
document.write( "                    _________\r\n" );
document.write( "                   /  x+4   /|\r\n" );
document.write( "  ______          /        / |\r\n" );
document.write( " /  x  /|        /________/  |\r\n" );
document.write( "/_____/ |       |         |  |\r\n" );
document.write( "| 2nd | |       |  1st    |  | \r\n" );
document.write( "|cube | /       |  cube   | /\r\n" );
document.write( "|_____|/        |_________|/\r\n" );
document.write( "\r\n" );
document.write( "V = x3            V = (x+4)3\r\n" );
document.write( "\r\n" );
document.write( ">>...The volumes of the cubes differ by 316 cm3...<<\r\n" );
document.write( "\r\n" );
document.write( "So \r\n" );
document.write( "\r\n" );
document.write( "      [Volume of 1st cube] MINUS [Volume of 2nd cube] = 316 c3\r\n" );
document.write( "\r\n" );
document.write( "               (x+4)3        -          x3            = 316\r\n" );
document.write( "\r\n" );
document.write( "                                                (x+4)3 - x3 = 316            \r\n" );
document.write( "Write 1st term as 3 factors:\r\n" );
document.write( "                                       (x+4)(x+4)(x+4) - x3 = 316\r\n" );
document.write( "FOIL out the first two:\r\n" );
document.write( "                                     (x2+4x+4x+16)(x+4) - x3 = 316\r\n" );
document.write( "Combine middle two terms:\r\n" );
document.write( "                                        (x2+8x+16)(x+4) - x3 = 316\r\n" );
document.write( "Multiply each term in 1st\r\n" );
document.write( "parentheses by each term is 2nd:  x3+4x2+8x2+32x+16x+64 - x3 = 316\r\n" );
document.write( "\r\n" );
document.write( "Combine like terms:                      x3+12x2+48x+64 - x3 = 316\r\n" );
document.write( "\r\n" );
document.write( "x3 and -x3 cancel out                            12x2+48x+64 = 316\r\n" );
document.write( "\r\n" );
document.write( "Subtract 316 from both sides\r\n" );
document.write( "to get 0 on the right                          12x2+48x-252 = 0    \r\n" );
document.write( "\r\n" );
document.write( "Factor out 12                                  12(x2+4x-21) = 0\r\n" );
document.write( "\r\n" );
document.write( "Factor the trinomial                           12(x+7)(x-3) = 0\r\n" );
document.write( "\r\n" );
document.write( "Set each factor with a variable = 0         \r\n" );
document.write( "Set first factor with a variable = 0            x+7 = 0                       \r\n" );
document.write( "                                                  x = -7\r\n" );
document.write( "\r\n" );
document.write( "Set first factor with a variable = 0            x-3 = 0                       \r\n" );
document.write( "                                                  x = 3\r\n" );
document.write( "\r\n" );
document.write( "Discard the negative answer.  Answer: smaller cube has edge = 3cm.\r\n" );
document.write( "                                      larger cube has edge 3+4 or 7 cm.  \r\n" );
document.write( "Edwin\r\n" );
document.write( "AnlytcPhil@aol.com
\n" ); document.write( "
\n" );