document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=965752>Question 965752</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help me solve this question:A cone with the sector angle of 45 degree is cut out of a circle of radius rcm.Find the base radius of the cone. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #590272 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=590272\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you cut out a sector of 45 degrees from the larger circle.\r<BR>\n" );
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document.write( "the length of the arc of that sector is equal to 1/8 times the circumference of the larger circle.\r<BR>\n" );
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document.write( "this is because arc length = 45/360 * 2*pi*r which makes arc length equal to 1/8 * 2*pi*r.\r<BR>\n" );
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document.write( "the arc length of the sector that you just cut out is the circumference of the base circle of the cone.\r<BR>\n" );
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document.write( "since the circumference of the base circle of the cone is 1/8 times the circumference of the larger circle, then it stands to reason that the radius of the base circle of the cone should be equal to 1/8 times the radius of the larger circle.\r<BR>\n" );
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document.write( "let r1 = the radius of the base circle of the cone.<BR>\n" );
document.write( "let r2 = the radius of the larger circle.\r<BR>\n" );
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document.write( "c1 = circumference of the base circle of the cone.<BR>\n" );
document.write( "c2 = circumference of the larger circle.\r<BR>\n" );
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document.write( "c1 = 2*pi*r1<BR>\n" );
document.write( "c2 = 2*pi*r2\r<BR>\n" );
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document.write( "since c2 is equal to 8 times c1, we get:\r<BR>\n" );
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document.write( "c1/c2 = 1/8 = (2*pi*r1) / (2*pi*r2)\r<BR>\n" );
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document.write( "since 2*pi in the numerator and denominator are the same, then cancel out, andyou are left with:\r<BR>\n" );
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document.write( "c1/c2 = 1/8 = r1/r2\r<BR>\n" );
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document.write( "the ratio of the circumference of the base circle to the larger circle is equla to 1/8 and the ratio of the radius of the base circle to the radius of the larger circle is also 1/8.\r<BR>\n" );
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document.write( "i believe that's what you're asking.\r<BR>\n" );
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document.write( "if it's any different, let me know.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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