document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117363>Question 117363</A>: <I><SPAN STYLE=\"word-break: break-all;\"> HI!<BR>\n" );
document.write( "please help me with this. I am really CLULESS on this question. <BR>\n" );
document.write( "Pineapple chunks are often packed in Cylindrical cans. If each can holds 500 ml determine <BR>\n" );
document.write( "a) The dimensions to one decimal place, of the can with minimum volume <BR>\n" );
document.write( "b) The cost to the nearest penny if the aluminum costs $ 0.2/ cm(squared) \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 #85447 by </B><A HREF=/tutors/aboutme.mpl?userid=psbhowmick><B>psbhowmick(878)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=psbhowmick><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=psbhowmick><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=85447\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Basically you have to find the relation between the radius and height of a right circular cylinder with given volume for minimum surface area.\r<BR>\n" );
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document.write( "Cans are hollow cylinders with both ends closed.<BR>\n" );
document.write( "So, total surface area is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+2%2Api%2Ar%5E2+%2B+2%2Api%2Ar%2Ah ALIGN=MIDDLE  ALT=\"S+=+2%2Api%2Ar%5E2+%2B+2%2Api%2Ar%2Ah\"   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%2Api%2Ar%28r+%2B+h%29 ALIGN=MIDDLE  ALT=\"S+=+2%2Api%2Ar%28r+%2B+h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The volume is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+pi%2Ar%5E2%2Ah ALIGN=MIDDLE  ALT=\"V+=+pi%2Ar%5E2%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+V%2F%28pi%2Ar%5E2%29 ALIGN=MIDDLE  ALT=\"h+=+V%2F%28pi%2Ar%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+2%2Api%2Ar%28r+%2B+V%2F%28pi%2Ar%5E2%29%29 ALIGN=MIDDLE  ALT=\"S+=+2%2Api%2Ar%28r+%2B+V%2F%28pi%2Ar%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > [substituting the value of 'h']<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+2pi%2Ar%5E2+%2B+2V%2Fr ALIGN=MIDDLE  ALT=\"S+=+2pi%2Ar%5E2+%2B+2V%2Fr\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "For minimum surface area,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dS%2Fdr+=+0 ALIGN=MIDDLE  ALT=\"dS%2Fdr+=+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%2Api%2Ar+-+2V%2Fr%5E2+=+0 ALIGN=MIDDLE  ALT=\"4%2Api%2Ar+-+2V%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+=+root%283%2CV%2F%282%2Api%29%29 ALIGN=MIDDLE  ALT=\"r+=+root%283%2CV%2F%282%2Api%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, the height is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+V%2F%28pi%2A%28root%283%2CV%2F%282%2Api%29%29%29%5E2%29 ALIGN=MIDDLE  ALT=\"h+=+V%2F%28pi%2A%28root%283%2CV%2F%282%2Api%29%29%29%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+=+V%2F%28pi%2Aroot%283%2CV%5E2%2F%284%2Api%5E2%29%29%29 ALIGN=MIDDLE  ALT=\"h+=+V%2F%28pi%2Aroot%283%2CV%5E2%2F%284%2Api%5E2%29%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=h+=+root%283%2C4V%2Fpi%29 ALIGN=MIDDLE  ALT=\"h+=+root%283%2C4V%2Fpi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "a) Substituting V = 500 cc,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+root%283%2C500%2F%282%2Api%29%29+=+4.30 ALIGN=MIDDLE  ALT=\"r+=+root%283%2C500%2F%282%2Api%29%29+=+4.30\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+root%283%2C4%2A500%2Fpi%29+=+8.60 ALIGN=MIDDLE  ALT=\"h+=+root%283%2C4%2A500%2Fpi%29+=+8.60\"   DISABLED_style= \"max-width:90%; height:auto;\" > cm\r<BR>\n" );
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document.write( "b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+2%2Api%2A4.3%284.3+%2B+8.6%29+=+348.53 ALIGN=MIDDLE  ALT=\"S+=+2%2Api%2A4.3%284.3+%2B+8.6%29+=+348.53\"   DISABLED_style= \"max-width:90%; height:auto;\" > sq cm<BR>\n" );
document.write( "So, cost of material per can = $(0.2 x 348.53) = $69.7. </SPAN>\n" );
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