document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205156>Question 1205156</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A piece of copper is described  below:\r<BR>\n" );
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document.write( "4 in. in length.\r<BR>\n" );
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document.write( "2 in. wide.\r<BR>\n" );
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document.write( ".5 in. thick.\r<BR>\n" );
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document.write( "The piece is formed into a wire of uniform thickness and 100 yds. in length.\r<BR>\n" );
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document.write( "Determine wire diameter.\r<BR>\n" );
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document.write( "Not sure how to solve.\r<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 #841805 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=841805\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "1 yard = 3 feet<BR>\n" );
document.write( "1 foot = 1/3 of a yard<BR>\n" );
document.write( "12 inches = 1/3 of a yard<BR>\n" );
document.write( "1 inch = (1/12)*(1/3) of a yard<BR>\n" );
document.write( "1 inch = 1/36 of a yard\r<BR>\n" );
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document.write( "Or you could say<BR>\n" );
document.write( "1 ft = 12 inches<BR>\n" );
document.write( "3 ft = 36 inches = 1 yard<BR>\n" );
document.write( "36 inches = 1 yard<BR>\n" );
document.write( "1 inch = 1/36 of a yard\r<BR>\n" );
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document.write( "Use that last equation to find that<BR>\n" );
document.write( "4 inches = 4/36 = 1/9 of a yard<BR>\n" );
document.write( "2 inches = 2/36 = 1/18 of a yard<BR>\n" );
document.write( "0.5 inches = 0.5/36 = 1/72 of a yard\r<BR>\n" );
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document.write( "Then,<BR>\n" );
document.write( "volume = (1/9)*(1/18)*(1/72)<BR>\n" );
document.write( "volume = 0.00008573 cubic yards\r<BR>\n" );
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document.write( "The wire formed is a cylinder of length 100 yards and radius r.<BR>\n" );
document.write( "volume of cylinder = pi*(radius)^2*(height)<BR>\n" );
document.write( "V = pi*r^2*h<BR>\n" );
document.write( "V = pi*r^2*100<BR>\n" );
document.write( "V = 100pi*r^2<BR>\n" );
document.write( "100pi*r^2 = 0.00008573<BR>\n" );
document.write( "r^2 = 0.00008573/(100pi)<BR>\n" );
document.write( "r^2 = 0.000 000 272 887<BR>\n" );
document.write( "r = sqrt(0.000 000 272 887)<BR>\n" );
document.write( "r = 0.0005223858727033<BR>\n" );
document.write( "d = diameter<BR>\n" );
document.write( "d = 2*r<BR>\n" );
document.write( "d = 2*0.0005223858727033<BR>\n" );
document.write( "d = 0.001044771745407<BR>\n" );
document.write( "This measure is in yards.\r<BR>\n" );
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document.write( "Multiply by 36 to convert from yards to inches. <BR>\n" );
document.write( "You should get roughly 0.03761178 inches.\r<BR>\n" );
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document.write( "Another approach:\r<BR>\n" );
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document.write( "volume of initial slab = 4*2*0.5 = 4 cubic inches.\r<BR>\n" );
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document.write( "1 yard = 36 inches, which means we multiply by 36 to convert from yards to inches.<BR>\n" );
document.write( "100 yards = 100*36 = 3600 inches.\r<BR>\n" );
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document.write( "Volume of a cylinder = pi*(radius)^2*(height)<BR>\n" );
document.write( "V = pi*r^2*h<BR>\n" );
document.write( "V = pi*r^2*3600<BR>\n" );
document.write( "V = 3600pi*r^2\r<BR>\n" );
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document.write( "3600pi*r^2 = 4<BR>\n" );
document.write( "r^2 = 4/(3600pi)<BR>\n" );
document.write( "r^2 = 0.0003 5368<BR>\n" );
document.write( "r = sqrt(0.0003 5368)<BR>\n" );
document.write( "r = 0.01880638<BR>\n" );
document.write( "d = 2*r<BR>\n" );
document.write( "d = 2*0.01880638<BR>\n" );
document.write( "d = 0.03761276<BR>\n" );
document.write( "We get roughly the same diameter as before. There's a bit of rounding error but the 0.03761 part is the same.\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "Wire diameter = <font color=red size=4>0.03761 inches</font> (approximate)<BR>\n" );
document.write( "Round this value however needed.<BR>\n" );
document.write( "It makes more sense to report the answer in inches rather than yards. But feel free to use yards instead if your teacher requires it.<BR>\n" );
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