document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207300>Question 1207300</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A company that manufactures dog food wishes to pack in closed cylindrical tins.<BR>\n" );
document.write( "What should be the dimensions of each tin if it is to have a volume of 128πcm³<BR>\n" );
document.write( "and the minimum possible surface area?  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #845091 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=845091\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The volume of the cylindrical can with radius r and height h is to be 128pi cm^3:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=%28pi%29r%5E2h=128pi ALIGN=MIDDLE  ALT=\"V=%28pi%29r%5E2h=128pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > [1]<br><BR>\n" );
document.write( "The surface area of the can -- top, bottom, and side -- is<br><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;\" > [2]<br><BR>\n" );
document.write( "Solve [1] for h in terms of r and substitute in [2] to get an expression for the surface area in terms of the single variable r:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=128%2Fr%5E2 ALIGN=MIDDLE  ALT=\"h=128%2Fr%5E2\"   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%28128%2Fr%5E2%29=2%28pi%29r%5E2%2B256%28pi%29%2Fr ALIGN=MIDDLE  ALT=\"S=2%28pi%29r%5E2%2B2%28pi%29r%28128%2Fr%5E2%29=2%28pi%29r%5E2%2B256%28pi%29%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Find the derivative of the expression for the surface area and set it equal to zero to find the radius r that minimizes the surface area:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dS%2Fdr=4%28pi%29r-256%28pi%29%2Fr%5E2 ALIGN=MIDDLE  ALT=\"dS%2Fdr=4%28pi%29r-256%28pi%29%2Fr%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28pi%29r-256%28pi%29%2Fr%5E2=0 ALIGN=MIDDLE  ALT=\"4%28pi%29r-256%28pi%29%2Fr%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28pi%29%28r-64%2Fr%5E2%29=0 ALIGN=MIDDLE  ALT=\"4%28pi%29%28r-64%2Fr%5E2%29=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r-64%2Fr%5E2=0 ALIGN=MIDDLE  ALT=\"r-64%2Fr%5E2=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E3-64=0 ALIGN=MIDDLE  ALT=\"r%5E3-64=0\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=4 ALIGN=MIDDLE  ALT=\"r=4\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The radius that minimizes the surface area is r=4; the corresponding height is 128/r^2 = 128/16 = 8.<br><BR>\n" );
document.write( "ANSWER: radius 4cm, height 8cm<br><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );