document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117465>Question 117465</A>: <I><SPAN STYLE=\"word-break: break-all;\"> hI1<BR>\n" );
document.write( "please help me with this. I have done so many questions before but this one just doesnt give the right answer?? any help would be apreciated\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The volume of a library is 20000 m (cubed) We have to minimize the Surface area to ignore the heat loss.Dtermine the dimensions of the building that will best give us teh minimum Surface area.??\r<BR>\n" );
document.write( "\n" );
document.write( "thanks for any help coming this way. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85472 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=85472\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For a cylindrical room, h is height, r is the radius.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+%28pi%29r%5E2h ALIGN=MIDDLE  ALT=\"V+=+%28pi%29r%5E2h\"   DISABLED_style= \"max-width:90%; height:auto;\" > Volume of the cylinder<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+2%28pi%29r%5E2%2B2%28pi%29rh ALIGN=MIDDLE  ALT=\"S+=+2%28pi%29r%5E2%2B2%28pi%29rh\"   DISABLED_style= \"max-width:90%; height:auto;\" > Surface area of top and bottom plus unrolled side<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=20000=%28pi%29r%5E2h ALIGN=MIDDLE  ALT=\"V=20000=%28pi%29r%5E2h\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You can rearrange the equation to solve for h as a function of r. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=20000%2F%28%28pi%29r%5E2%29 ALIGN=MIDDLE  ALT=\"h=20000%2F%28%28pi%29r%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "Then substitute that back into the surface area equation,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+2%28pi%29r%5E2%2B2%28pi%29rh ALIGN=MIDDLE  ALT=\"S+=+2%28pi%29r%5E2%2B2%28pi%29rh\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+2%28pi%29r%5E2%2B2%28pi%29r%2820000%2F%28%28pi%29r%5E2%29%29 ALIGN=MIDDLE  ALT=\"S+=+2%28pi%29r%5E2%2B2%28pi%29r%2820000%2F%28%28pi%29r%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+2%28pi%29r%5E2%2B40000%2Fr ALIGN=MIDDLE  ALT=\"S+=+2%28pi%29r%5E2%2B40000%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Plot S using various values of r and look for a minimum.<BR>\n" );
document.write( "8.1,	5350.<BR>\n" );
document.write( "9.1,	4915.<BR>\n" );
document.write( "10.1,	4601.<BR>\n" );
document.write( "11.1,	4377.<BR>\n" );
document.write( "12.1,	4225.<BR>\n" );
document.write( "13.1,	4131.<BR>\n" );
document.write( "14.1,	4085.<BR>\n" );
document.write( "15.1,	4080.<BR>\n" );
document.write( "16.1,	4112.<BR>\n" );
document.write( "17.1,	4175.<BR>\n" );
document.write( "18.1,	4267.<BR>\n" );
document.write( "19.1,	4385.<BR>\n" );
document.write( "20.1,	4527.<BR>\n" );
document.write( "Looks like a minimum at r=15.1.<BR>\n" );
document.write( "Now that you have r, go back to your equation for h and solve. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=20000%2F%28%28pi%29r%5E2%29 ALIGN=MIDDLE  ALT=\"h=20000%2F%28%28pi%29r%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=20000%2F%28%28pi%2915.1%5E2%29 ALIGN=MIDDLE  ALT=\"h=20000%2F%28%28pi%2915.1%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=27.9%29 ALIGN=MIDDLE  ALT=\"h=27.9%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Make sure to check your answer. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+%28pi%29r%5E2h ALIGN=MIDDLE  ALT=\"V+=+%28pi%29r%5E2h\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+%28pi%2915.1%5E2%2A27.9 ALIGN=MIDDLE  ALT=\"V+=+%28pi%2915.1%5E2%2A27.9\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+19985 ALIGN=MIDDLE  ALT=\"V+=+19985\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Close enough. <BR>\n" );
document.write( "r=15.1 m, h=27.9 m </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );