document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=118675>Question 118675</A>: <I><SPAN STYLE=\"word-break: break-all;\"> This is a gre math problem....\r<BR>\n" );
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document.write( "a certain cake recipe states that the cake should be baked in a pan 8 inches in diameter.  If Julie wants to use the recipe to make a cake of the same depth but 12 inches in diameter, by what factor should she muiltiply the ingredients?\r<BR>\n" );
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document.write( "my answer: 1.5  but this is wrong and statistics show that over 65% of the people taking the test got this wrong answer...\r<BR>\n" );
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document.write( "The correct answer is 2.25...why???  \r<BR>\n" );
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document.write( "If you can help, thanks! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #86802 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=86802\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Cake batter volume is the real variable that you're interested in here. <BR>\n" );
document.write( "With a larger pan, you need more batter.<BR>\n" );
document.write( "With a smaller pan, you need less batter.<BR>\n" );
document.write( "For the same volume, you will have a definite relationship between the height and diamter.  <BR>\n" );
document.write( "The volume of the cake batter depends on the diameter of the pan and on the height of the pan. <BR>\n" );
document.write( "For a cylindrical pan, the volume is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=%28pi%29%2AD%5E2%2F4%2Ah ALIGN=MIDDLE  ALT=\"V=%28pi%29%2AD%5E2%2F4%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Originally let's use the subscript 1 to refer to 8 inch diameter pan.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5B1%5D=%28pi%29%2AD%5B1%5D%5E2%2F4%2Ah%5B1%5D ALIGN=MIDDLE  ALT=\"V%5B1%5D=%28pi%29%2AD%5B1%5D%5E2%2F4%2Ah%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "When it's a 12 inch diameter pan let's use subscript 2.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5B2%5D=%28pi%29%2AD%5B2%5D%5E2%2F4%2Ah%5B2%5D ALIGN=MIDDLE  ALT=\"V%5B2%5D=%28pi%29%2AD%5B2%5D%5E2%2F4%2Ah%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now let's plug in some numbers.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5B1%5D=%28pi%29%2A8%5E2%2F4%2Ah%5B1%5D ALIGN=MIDDLE  ALT=\"V%5B1%5D=%28pi%29%2A8%5E2%2F4%2Ah%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5B1%5D=%28pi%29%2A64%2F4%2Ah%5B1%5D ALIGN=MIDDLE  ALT=\"V%5B1%5D=%28pi%29%2A64%2F4%2Ah%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5B1%5D=16%2A%28pi%29%2Ah%5B1%5D ALIGN=MIDDLE  ALT=\"V%5B1%5D=16%2A%28pi%29%2Ah%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "And for pan 2,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5B2%5D=%28pi%29%2AD%5B2%5D%5E2%2F4%2Ah%5B2%5D ALIGN=MIDDLE  ALT=\"V%5B2%5D=%28pi%29%2AD%5B2%5D%5E2%2F4%2Ah%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5B2%5D=%28pi%29%2A12%5E2%2F4%2Ah%5B2%5D ALIGN=MIDDLE  ALT=\"V%5B2%5D=%28pi%29%2A12%5E2%2F4%2Ah%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5B2%5D=36%2A%28pi%29%2Ah%5B2%5D ALIGN=MIDDLE  ALT=\"V%5B2%5D=36%2A%28pi%29%2Ah%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Also, remember the depth is the same. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5B1%5D=h%5B2%5D=h ALIGN=MIDDLE  ALT=\"h%5B1%5D=h%5B2%5D=h\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5B1%5D=16%2A%28pi%29%2Ah ALIGN=MIDDLE  ALT=\"V%5B1%5D=16%2A%28pi%29%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "2.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5B2%5D=36%2A%28pi%29%2Ah ALIGN=MIDDLE  ALT=\"V%5B2%5D=36%2A%28pi%29%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "of re-writing the equation 2.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=V%5B2%5D%2F%2836%2A%28pi%29%29 ALIGN=MIDDLE  ALT=\"h=V%5B2%5D%2F%2836%2A%28pi%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now plug that value back into equation 1.<BR>\n" );
document.write( "1.<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5B1%5D=16%2A%28pi%29%2Ah ALIGN=MIDDLE  ALT=\"V%5B1%5D=16%2A%28pi%29%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5B1%5D=16%2A%28pi%29%2AV%5B2%5D%2F%2836%2A%28pi%29%29 ALIGN=MIDDLE  ALT=\"V%5B1%5D=16%2A%28pi%29%2AV%5B2%5D%2F%2836%2A%28pi%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=V%5B2%5D=%2836%2F16%29%2AV%5B1%5D ALIGN=MIDDLE  ALT=\"V%5B2%5D=%2836%2F16%29%2AV%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5B2%5D=2.25%2AV%5B1%5D ALIGN=MIDDLE  ALT=\"V%5B2%5D=2.25%2AV%5B1%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So you need 2.25 times as much batter, so you multply all of the batter ingredients by 2.25.  </SPAN>\n" );
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