document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=969172>Question 969172</A>: <I><SPAN STYLE=\"word-break: break-all;\"> You have been asked to design a can shaped like a right circular cylinder with height h and radius r. Given that the can must hold exactly 410 cm^3, what values of h and r will minimise the total surface area (including the top and bottom faces)? Give your answers correct to 2 decimal places as a list [in brackets] of the form: [ h, r ] <BR>\n" );
document.write( "for constants h (height), r (radius), in that order.\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 #592171 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=592171\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i couldn't find any other way to do it without using calculus, so i solved it by graphing.\r<BR>\n" );
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document.write( "i got r = 4.025946 and h = 8.051894821.\r<BR>\n" );
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document.write( "with those values, surface area = 2 * pi * r * h + 2 * p * r^2 = 305.51822\r<BR>\n" );
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document.write( "the graph of the equation for surface area looks like this.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/050801.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the formula for surface area used was:\r<BR>\n" );
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document.write( "y = 2 * pi * x * (410/(pi * x^2)) + 2 * pi * x^2\r<BR>\n" );
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document.write( "y represents the surface area.<BR>\n" );
document.write( "x represents the radius.<BR>\n" );
document.write( "h is equal to (410 / (pi * r^2))\r<BR>\n" );
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document.write( "this was derived by solving for h in the volume formuls of v = pi * r^2 * h.\r<BR>\n" );
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document.write( "when v is equal to 410, this formula became 410 = pi * r^2 * h.\r<BR>\n" );
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document.write( "this led to h = (410 / (pi * r^2)).\r<BR>\n" );
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document.write( "the formula could have been simplified further but i left it the way it was so you could see the value of h in terms of r stand out more clearly.\r<BR>\n" );
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document.write( "the area on the graph of interest is when x and y are both greater than 0.\r<BR>\n" );
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