document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203201>Question 1203201</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A Metal Sleeve Of Length 20 Cm Has Rectangular Cross-Section 10 Cm By 8 Cm. The Metal Has Uniform Thickness, Xcm, Along The Sleeve, And The Total Volume Of metal in the sleeve is 495cm3. Derive the equation 16x^2-144x+99=0. <BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838569 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=838569\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "A Metal Sleeve Of Length 20 Cm Has Rectangular Cross-Section 10 Cm By 8 Cm (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28outer_dimensions%29 ALIGN=MIDDLE  ALT=\"highlight%28outer_dimensions%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >). <BR>\n" );
document.write( "The Metal Has Uniform Thickness, x cm, Along The Sleeve, And The Total Volume Of metal in the sleeve is 495 cm3. <BR>\n" );
document.write( "Derive the equation 16x^2-144x+99=0. <BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "The outer dimensions of the sleeve are 10 cm by 8 cm.\r\n" );
document.write( "The metallic walls have thickness of x cm, uniformly.\r\n" );
document.write( "So, the empty space in cross-section has dimensions (10-2x) cm by (8-2x) cm.\r\n" );
document.write( "We subtract 2x to account for the thickness of the two walls in each direction.\r\n" );
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document.write( "Therefore, the area of the metal in cross-section is\r\n" );
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document.write( "    area = 10*8 - (10-2x)*(8-2x) cm^2.\r\n" );
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document.write( "    +---------------------------------------------------------+\r\n" );
document.write( "    |    Since the length is 20 cm, the volume of the metal   |\r\n" );
document.write( "    |        is 20 times the area of the cross-section.       |\r\n" );
document.write( "    +---------------------------------------------------------+\r\n" );
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document.write( "So, your equation for x is\r\n" );
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document.write( "    -20*(4x^2 - 36x) = 495  cm^3.\r\n" );
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document.write( "Divide both sides by 5 and simplify further step by step.\r\n" );
document.write( "</PRE>\r<BR>\n" );
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document.write( "Nice exercise for you to complete it on your own.\r<BR>\n" );
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document.write( "You may report me about your progress.\r<BR>\n" );
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document.write( "To see many other similar problems, look into the lessons\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Surface-area/Problems-on-the-area-of-a-rectangle-surrounded-by-a-strip.lesson>Problems on the area and the dimensions of a rectangle surrounded by a strip</A>\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Surface-area/Cynthia-Besch-and-the-rug.lesson>Cynthia Besch wants to buy a rug for a room</A> \r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;- <A  rel=nofollow HREF=https://www.algebra.com/algebra/homework/Surface-area/Circular-pool-and-a-walkway-around.lesson>Problems on a circular pool and a walkway around it</A>\r<BR>\n" );
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document.write( "in this site.\r<BR>\n" );
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document.write( "After reading these lessons, you will feel yourself very confident with such problems.\r<BR>\n" );
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