document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=167479>Question 167479</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, i was given a problem by my teacher and did not understand it:\r<BR>\n" );
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document.write( "When 0.5 cm was planed off of each of the 6 faces of a wooden cube its volume decreased by 169 cm^2. Find its new volume. \r<BR>\n" );
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document.write( "Thank You. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #123368 by </B><A HREF=/tutors/aboutme.mpl?userid=nerdybill><B>nerdybill(7384)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=nerdybill><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=nerdybill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=123368\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When 0.5 cm was planed off of each of the 6 faces of a wooden cube its voume decreased by 169 cm^2. Find its new volume. <BR>\n" );
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document.write( "A \"cube\" implies that all edges are the same length.<BR>\n" );
document.write( "Volume of a cube is \"length of an edge\" cubed.<BR>\n" );
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document.write( "Let x = original length of one edge<BR>\n" );
document.write( "then<BR>\n" );
document.write( "x-1 = edge of new cube<BR>\n" );
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document.write( "x^3 - 169 = (x-1)^3<BR>\n" );
document.write( "x^3 - 169 = (x-1)(x-1)(x-1)<BR>\n" );
document.write( "x^3 - 169 = (x^2-2x+1)(x-1)<BR>\n" );
document.write( "x^3 - 169 = (x)(x^2-2x+1)-(x^2-2x+1)<BR>\n" );
document.write( "x^3 - 169 = (x^3-2x^2+x)-(x^2-2x+1)<BR>\n" );
document.write( "x^3 - 169 = x^3-2x^2+x-x^2+2x-1<BR>\n" );
document.write( "x^3 - 169 = x^3-3x^2+x+2x-1<BR>\n" );
document.write( "x^3 - 169 = x^3-3x^2+3x-1<BR>\n" );
document.write( "-169 = -3x^2+3x-1<BR>\n" );
document.write( "0 = -3x^2+3x+168<BR>\n" );
document.write( "dividing both sides by 3:<BR>\n" );
document.write( "0 = -x^2+x+56<BR>\n" );
document.write( "0 = x^2-x-56<BR>\n" );
document.write( "0 = (x-8)(x+7)<BR>\n" );
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document.write( "x = {-7, 8}<BR>\n" );
document.write( "We can toss out the negative solution so we end up with:<BR>\n" );
document.write( "x = 8 cm (length of an edge of the original cube)<BR>\n" );
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document.write( "Length of new cube edge:<BR>\n" );
document.write( "x-1 = 8-1 = 7 cm<BR>\n" );
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document.write( "Finally, volume of new cube is:<BR>\n" );
document.write( "7^3 = 343 cubic cm\r<BR>\n" );
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