document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=356749>Question 356749</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the area of a circle whose circumference is 1/3 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #254665 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=254665\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> c = 2*pi*r is the formula for the circumference of a circle.\r<BR>\n" );
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document.write( "since c = 1/3, this means that:\r<BR>\n" );
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document.write( "1/3 = 2*pi*r\r<BR>\n" );
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document.write( "divide both sides of this equation by 2*pi to get:\r<BR>\n" );
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document.write( "r = 1/(6*pi)\r<BR>\n" );
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document.write( "a = pi*r^2 is the formula for the area of a circle.\r<BR>\n" );
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document.write( "since r = 1/(6*pi), then:\r<BR>\n" );
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document.write( "r^2 = (1/(6*pi)^2 = (1^2) / (6*pi)^2 = 1 / (36*pi^2)\r<BR>\n" );
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document.write( "since a = pi*r^2, substitute for r^2 to get:\r<BR>\n" );
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document.write( "a = pi*(1/(36*pi^2) which is the same as (pi/(36*pi^2) which simplifies to:\r<BR>\n" );
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document.write( "a = 1 / (36*pi)\r<BR>\n" );
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document.write( "we can solve backwards to find r again.\r<BR>\n" );
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document.write( "a = pi * r^2\r<BR>\n" );
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document.write( "this makes (1/(36*pi) = pi*r^2\r<BR>\n" );
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document.write( "if we multiply both sides of this equation by pi, we get:\r<BR>\n" );
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document.write( "1/36 = pi^2 * r^2\r<BR>\n" );
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document.write( "if we take the square root of both sides of this equation, we get:\r<BR>\n" );
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document.write( "1/6 = pi*r\r<BR>\n" );
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document.write( "if we multiply both sides of this equation by 2, we get:\r<BR>\n" );
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document.write( "1/3 = 2*pi*r\r<BR>\n" );
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document.write( "we worked our way back from the area equation to the circumference equation, so we should be good.\r<BR>\n" );
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document.write( "your answer should be:\r<BR>\n" );
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document.write( "a = 1 / (36*pi) </SPAN>\n" );
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