document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172878>Question 1172878</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The slant height of a cone is doubled. Does this double the surface area of the cone? Explain your<BR>\n" );
document.write( "reasoning. </SPAN>\n" );
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document.write( "The lateral surface area of a cone is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28pi%29%28r%29%28l%29 ALIGN=MIDDLE  ALT=\"%28pi%29%28r%29%28l%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, where r is the radius of the base and <i>l</i> is the slant height.<br><BR>\n" );
document.write( "The area of the base is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28pi%29%28r%5E2%29 ALIGN=MIDDLE  ALT=\"%28pi%29%28r%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "The intent of the question is not clear....<br><BR>\n" );
document.write( "(1) If only the slant height of the cone is doubled (the radius of the cone is unchanged), then the LATERAL surface area is doubled.  The (total) surface area of the cone -- which is literally what the question asks for, is NOT doubled, because the surface area of the base does not change.<br><BR>\n" );
document.write( "(2) If the \"new\" cone is similar to the original -- which means the slant height and radius are both doubled, then we have two similar solids with scale factor 2; the ratio of surface areas is 4:1.  So in this case the surface area is multiplied by a factor of 4, not 2.<br><BR>\n" );
document.write( "ANSWER: Yes, the surface area is doubled -- IF only the slant height is doubled AND by \"surface area\" you are only talking about LATERAL surface area.<br><BR>\n" );
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