document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=252787>Question 252787</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The diameter of the large circle is twice the diameter of the small circle. What is the ratio of their areas?\r<BR>\n" );
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document.write( "A) 1:2  B) 1:3  C) 1:4  D) 1:5  E) 1:6 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #184863 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=184863\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the radius of a circle is equal to (1/2) * the diameter of the circle.\r<BR>\n" );
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document.write( "let the diameter of the smaller circle = 2 * r<BR>\n" );
document.write( "this makes the radius of the smaller circle = r\r<BR>\n" );
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document.write( "since the diameter of the larger circle is 2 times the diameter of the smallet circle:\r<BR>\n" );
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document.write( "this makes the diameter of the larger circle = 4 * r<BR>\n" );
document.write( "this makes the radius of the larger circle = 2 * r\r<BR>\n" );
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document.write( "area of the smaller circle = 2 * pi * r^2<BR>\n" );
document.write( "area of the larger circle = 2 * pi * (2 * r)^2 = 2 * pi * 4 * r^2 = 8 * pi * r^2\r<BR>\n" );
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document.write( "area of smaller circle / area of larger circle becomes:\r<BR>\n" );
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document.write( "2 * pi * r^2 / 8 * pi * r^2\r<BR>\n" );
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document.write( "pi * r^2 cancel out so you get 2 / 8 which simplified to 1 / 4.\r<BR>\n" );
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document.write( "ratio of area of smaller circle to larger circle is 1 / 4 = 1:4.\r<BR>\n" );
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document.write( "answer is selection C (1:4).\r<BR>\n" );
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document.write( "example:\r<BR>\n" );
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document.write( "let diameter of smaller circle = 6.<BR>\n" );
document.write( "radius of smaller circle is 3 and area of smaller circle is 2 * pi * 3^2 = 2 * pi * 9 = 56.54866776\r<BR>\n" );
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document.write( "diameter of larger circle = 2 * 6 = 12<BR>\n" );
document.write( "radius of larger circle is 6 and area of larger circle is 2 * pi * 6^2 = 2 * pi * 36 = 226.1946711\r<BR>\n" );
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document.write( "ratio of area of smaller circle to area of larger circle equals:\r<BR>\n" );
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document.write( "56.54866775/226.1946711 = .25 = 1/4.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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