document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1033470>Question 1033470</A>: <I><SPAN STYLE=\"word-break: break-all;\"> a closed cylindrical tin is required to contain 500cc\r<BR>\n" );
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document.write( " show that an equation for the total external surface area of the tin is area= 1000/r + 2pir^2\r<BR>\n" );
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document.write( "find the height and the diameter of the can so as to use the minimum amount of metal? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #648100 by </B><A HREF=/tutors/aboutme.mpl?userid=Cromlix><B>Cromlix(4381)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Cromlix><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=Cromlix><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=648100\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Hi there,<BR>\n" );
document.write( "&#960; x r^2 x h = 500cc<BR>\n" );
document.write( "h = 500/&#960;r^2<BR>\n" );
document.write( "Surface Area:<BR>\n" );
document.write( "&#960; x diameter x height + 2 x &#960; x r^2<BR>\n" );
document.write( "Using:<BR>\n" );
document.write( "h = 500/&#960;r^2<BR>\n" );
document.write( "&#960 x 2r (diameter)x 500/&#960;r^2<BR>\n" );
document.write( "Area = 1000/r + 2&#960;r^2<BR>\n" );
document.write( "Area = 1000r^-1 + 2&#960;r^2<BR>\n" );
document.write( "Area (differentiated) <BR>\n" );
document.write( "= -1000r^-2 + 4&#960;r<BR>\n" );
document.write( "-1000r^-2 + 4&#960;r = 0<BR>\n" );
document.write( "-1000/r^2 + 4&#960;r = 0<BR>\n" );
document.write( "-1000/r^2 = -4&#960;r (Multiply both sides by -1)<BR>\n" );
document.write( " 1000/r^2 = 4&#960;r <BR>\n" );
document.write( "1000 = 4&#960r^3<BR>\n" );
document.write( "Divide both sides by 4<BR>\n" );
document.write( "250 = &#960;r^3<BR>\n" );
document.write( "r^3 = 250/&#960;<BR>\n" );
document.write( "r = 3&#8730;250/&#960;<BR>\n" );
document.write( "r = 4.3<BR>\n" );
document.write( "..........<BR>\n" );
document.write( "Using Nature Table:       -   4.3   +<BR>\n" );
document.write( " .................. .......... .........                      \   -    /<BR>\n" );
document.write( "Minimum.<BR>\n" );
document.write( "...............<BR>\n" );
document.write( "To establish height and radius<BR>\n" );
document.write( "&#960;r^2h = 500<BR>\n" );
document.write( "&#960;(4.3)^2h = 500<BR>\n" );
document.write( "height = 500/(&#960;(4.3)^2<BR>\n" );
document.write( "Height = 8.6 centimeters<BR>\n" );
document.write( "Radius = 4.3 centimeters<BR>\n" );
document.write( "so, Diameter = 8.6 diameters.<BR>\n" );
document.write( "Hope this helps :-)<BR>\n" );
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document.write( " </SPAN>\n" );
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