document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1062609>Question 1062609</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The radii of two cones are in the ratio 5:7 calculate <BR>\n" );
document.write( "1. Area ratio<BR>\n" );
document.write( "2. volume ratio<BR>\n" );
document.write( "3.  if the volume of the smaller cone is 35cm3,  find the volume  of the larger one.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #677557 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=677557\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> if the ratio of the sides of 2 polygons is 5/7, then the ratio of the area of the two polygons is (5/7)^2 and the ratio of the volume of the two polygons is (5/7)^3.\r<BR>\n" );
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document.write( "the volume of your smaller polygon is 35 cm^3.\r<BR>\n" );
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document.write( "let x be the volume of your larger polygon.\r<BR>\n" );
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document.write( "then (5/7)^3 * x = 35\r<BR>\n" );
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document.write( "solve for x to get x = 96.04 cm^3.\r<BR>\n" );
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document.write( "the surface area of your polygon is divided into two parts.\r<BR>\n" );
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document.write( "the formula is equal to pi * r^2 + pi * r * l, where l is the small letter L which represents the slant height.\r<BR>\n" );
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document.write( "the ratio of the surface area of the smaller cone is therefore equal to (5/7)^2 * pi * r^2 + (5/7)^2 * pi * r * l.\r<BR>\n" );
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document.write( "this formula can be made equivalent to (5/7)^2 * (pi * r^2 + pi * r * l).\r<BR>\n" );
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document.write( "if this is correct, then the surface area of the smaller cone should be equal to (5/7)^2 * the surface area of the larger cone.\r<BR>\n" );
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document.write( "i tested this out with an online calculator and determined that it is correct.\r<BR>\n" );
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document.write( "you can do the same, using the following online calculator.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"http://ncalculators.com/area-volume/cone-calculator.htm\" target = \"_blank\">http://ncalculators.com/area-volume/cone-calculator.htm</a>\r<BR>\n" );
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document.write( "note that the calculator used the formula pi * r^2 + pi * r * sqrt(r^2 + h^2).\r<BR>\n" );
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document.write( "this is because l is equal to sqrt (r^2 + h^2), therefore, they just replace l with sqrt(r^2 + h^2).\r<BR>\n" );
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document.write( "the calculator confirms thqt the volume of the smaller cone is equal to (5/7)^3 * the volume of the larger cone, and it confirms that the surface area of the smaller cone is equal to (5/7)^2 * the area of the large cone.\r<BR>\n" );
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document.write( "i used the following measurements when testing.\r<BR>\n" );
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document.write( "radius of smaller cone is 5.<BR>\n" );
document.write( "height of smaller cone is 10.\r<BR>\n" );
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document.write( "radius of larger cone is 7.<BR>\n" );
document.write( "height of larger cone is 14.\r<BR>\n" );
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document.write( "you can see that the ratio of the corresponding sides are (5/7).\r<BR>\n" );
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document.write( "you can use whatever measures you see fit.\r<BR>\n" );
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document.write( "just make sure that the corresponding sides of the smaller cone are equal to 5/7 * the corresponding sides of the larger cone.<BR>\n" );
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