document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=477800>Question 477800</A>: <I><SPAN STYLE=\"word-break: break-all;\"> if the altitude of a right cylinder is doubled, what happens to its 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 #327410 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=327410\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if the altitude of a right cylinder is doubled, what happens to its surface area?<BR>\n" );
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document.write( "The SA of a cylinder of height h and radius r is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SA+=+pi%2Ar%2As ALIGN=MIDDLE  ALT=\"SA+=+pi%2Ar%2As\"   DISABLED_style= \"max-width:90%; height:auto;\" > where s = slant height<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s+=+sqrt%28r%5E2+%2B+h%5E2%29 ALIGN=MIDDLE  ALT=\"s+=+sqrt%28r%5E2+%2B+h%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=SA+=+pi%2Ar%2Asqrt%28r%5E2+%2B+h%5E2%29 ALIGN=MIDDLE  ALT=\"SA+=+pi%2Ar%2Asqrt%28r%5E2+%2B+h%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "If h is doubled:<BR>\n" );
document.write( "--> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ar%2Asqrt%28r%5E2+%2B+4h%5E2%29 ALIGN=MIDDLE  ALT=\"pi%2Ar%2Asqrt%28r%5E2+%2B+4h%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The ratio is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28r%5E2+%2B+4h%5E2%29%2Fsqrt%28r%5E2+%2B+h%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28r%5E2+%2B+4h%5E2%29%2Fsqrt%28r%5E2+%2B+h%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "The difference is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28r%5E2+%2B+4h%5E2%29+-+sqrt%28r%5E2+%2B+h%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28r%5E2+%2B+4h%5E2%29+-+sqrt%28r%5E2+%2B+h%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Neither the ratio nor the difference makes it obvious.<BR>\n" );
document.write( "If both the height and the radius are doubled, the SA is x4 (and the volume is x8).<BR>\n" );
document.write( "If one is doubled, the ratio is less than 4 and more than 2, but a quantitative answer depends on the values of r and h, or at least the ratio of r to h.<BR>\n" );
document.write( "If h were given to be equal to r and then doubled, a more definitive answer could be obtained.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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