document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=332495>Question 332495</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The volume of rectangular solid with a square base is 216 cubic inches.What is<BR>\n" );
document.write( "the least possible surface area for the solid?\r<BR>\n" );
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document.write( "(A) 24 in.2 (B) 72 in.2 (C) 216 in.2 (D) 252 in.2 (E) 492 in.2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #238282 by </B><A HREF=/tutors/aboutme.mpl?userid=jrfrunner><B>jrfrunner(365)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jrfrunner><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=jrfrunner><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=238282\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This requires knowing the equation of the volume and surface area of rectangles\r<BR>\n" );
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document.write( "volume: (area of base)*height, <BR>\n" );
document.write( "since base is a square and if its side is \"S\" then<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=volume+=+s%5E2%2AH ALIGN=MIDDLE  ALT=\"volume+=+s%5E2%2AH\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Surface area:  2* (area of the base) + (perimeter of the base) * height <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=Surface+Area+=2%2AS%5E2+%2B+4%2AS%2AH ALIGN=MIDDLE  ALT=\"Surface+Area+=2%2AS%5E2+%2B+4%2AS%2AH\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "====<BR>\n" );
document.write( "Solve the volume equation for H:   <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H=Volume%2F%28S%5E2%29 ALIGN=MIDDLE  ALT=\"H=Volume%2F%28S%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "substitute this into the surface area: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2AS%5E2%2B4%2AS%2AH+=+2%2AS%5E2+%2B+4%2AS%28Volume%2F%28S%5E2%29%29 ALIGN=MIDDLE  ALT=\"2%2AS%5E2%2B4%2AS%2AH+=+2%2AS%5E2+%2B+4%2AS%28Volume%2F%28S%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Surface area= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SA=2%2AS%5E2+%2B+4%2Avolume%2FS+=+2%2AS%5E2+%2B+4%2A%28216%29%2FS+=+2%2AS%5E2%2B864%2FS ALIGN=MIDDLE  ALT=\"SA=2%2AS%5E2+%2B+4%2Avolume%2FS+=+2%2AS%5E2+%2B+4%2A%28216%29%2FS+=+2%2AS%5E2%2B864%2FS\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "---<BR>\n" );
document.write( "Take the derivative of SA: (SA)' =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4%2AS+-864%2F%28S%5E2%29 ALIGN=MIDDLE  ALT=\"+4%2AS+-864%2F%28S%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "--<BR>\n" );
document.write( "set this derivative =0 and solve for S<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4S-864%2F%28S%5E2%29+=+0 ALIGN=MIDDLE  ALT=\"4S-864%2F%28S%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=4S=864%2F%28S%5E2%29 ALIGN=MIDDLE  ALT=\"4S=864%2F%28S%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=4S%5E3=864 ALIGN=MIDDLE  ALT=\"4S%5E3=864\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S%5E3=216 ALIGN=MIDDLE  ALT=\"S%5E3=216\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "S=6<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Check to see if this a minimum or maximum by taking the second derivative of SA<BR>\n" );
document.write( "(SA)\" =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+4-864%2A%28-2%29%2F%28S%5E3%29=4%2B3456%2F%28S%5E3%29 ALIGN=MIDDLE  ALT=\"+4-864%2A%28-2%29%2F%28S%5E3%29=4%2B3456%2F%28S%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > evaluated at S=6<BR>\n" );
document.write( "(SA)\"= <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2B3456%2F%286%5E3%29=20 ALIGN=MIDDLE  ALT=\"4%2B3456%2F%286%5E3%29=20\"   DISABLED_style= \"max-width:90%; height:auto;\" >, since its positive this means, the function curves upward, thus S=6 is a minimum<BR>\n" );
document.write( "---<BR>\n" );
document.write( "Now substitute S=6 into the SA equation to find the lowest surface area<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SA=+2%2AS%5E2%2B864%2FS+=+2%2A6%5E2%2B864%2F6=2%2A36%2B144=216 ALIGN=MIDDLE  ALT=\"SA=+2%2AS%5E2%2B864%2FS+=+2%2A6%5E2%2B864%2F6=2%2A36%2B144=216\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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