document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187599>Question 1187599</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A central angle 𝜃 in a circular garden of radius 20 meters is subtended by an arc of length 15𝜋 meters.<BR>\n" );
document.write( " a. What is the measure of 𝜃 in degrees? <BR>\n" );
document.write( " b. What is the area of the sector being described? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #818604 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=818604\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the radius of the garden is 20 meters.<BR>\n" );
document.write( "the circumference of the garden is 2 * pi * r = 40 * pi.<BR>\n" );
document.write( "the area of the garden is pi * r^2 = pi * 20^2 = 400 * pi.\r<BR>\n" );
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document.write( "the arc is 15 * pi.\r<BR>\n" );
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document.write( "the central angle of the arc is 15 * pi / (40 * pi) * 360 = 135 degrees.\r<BR>\n" );
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document.write( "the area of the sector is equal to 135/360 * 400 * pi = 150 * pi.\r<BR>\n" );
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document.write( "the circumference and the area of the sector of the circle are proportion to the central angle of the sector divided by 360 * the circumference of the circle and also times the area of the circle.\r<BR>\n" );
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document.write( "when the central angle of the sector is 135 degrees, then the fraction is 135/360.\r<BR>\n" );
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document.write( "the circumference of the circle is 2 * pi * 20 = 40 * pi.<BR>\n" );
document.write( "the area of the circle is pi * 20^2 = 400 * pi.\r<BR>\n" );
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document.write( "the arc of the sector is 135 / 360 * 40 * pi = 15 * pi.<BR>\n" );
document.write( "this is not surprising since we used the circumference of the circle and the length of the arc to find the central angle.\r<BR>\n" );
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document.write( "the area of the sector is 135 / 360 * 400 * pi = 150 * pi.\r<BR>\n" );
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document.write( "here's a reference on arc length of a sector and area of a sector.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://byjus.com/maths/sector-of-a-circle/\" target = \"_blank\">https://byjus.com/maths/sector-of-a-circle/</a>\r<BR>\n" );
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