document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=893080>Question 893080</A>: <I><SPAN STYLE=\"word-break: break-all;\"> What is the maximum area that can be enclosed by a wire of length 24 cm by bending it in the form of a sector of the circle ? <BR>\n" );
document.write( "Thank you sir. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #541080 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=541080\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> What is the maximum area that can be enclosed by a wire of length 24 cm by bending it in the form of a sector of the circle ? <BR>\n" );
document.write( ":<BR>\n" );
document.write( "let a = arc distance of the sector<BR>\n" );
document.write( "let r = radius of the circle<BR>\n" );
document.write( "then<BR>\n" );
document.write( "a + 2r = 24 <BR>\n" );
document.write( "a = (24-2r)<BR>\n" );
document.write( ":<BR>\n" );
document.write( "Find the portion of the circle in the sector (arc/circumference)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2F%282pi%2Ar%29 ALIGN=MIDDLE  ALT=\"a%2F%282pi%2Ar%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Replace a with (24-2r)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2824-2r%29%29%2F%282%2Api%2Ar%29 ALIGN=MIDDLE  ALT=\"%28%2824-2r%29%29%2F%282%2Api%2Ar%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "simplifies to<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2812-r%29%29%2F%28pi%2Ar%29 ALIGN=MIDDLE  ALT=\"%28%2812-r%29%29%2F%28pi%2Ar%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Find the area of the sector<BR>\n" );
document.write( "A = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2812-r%29%29%2F%28pi%2Ar%29 ALIGN=MIDDLE  ALT=\"%28%2812-r%29%29%2F%28pi%2Ar%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > * <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"pi%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Cancel pi*r<BR>\n" );
document.write( "A = (12-r) * r<BR>\n" );
document.write( "A = -r^2 + 12r<BR>\n" );
document.write( "Max of this quadratic equation occurs at the axis of symmetry; x=-b/(2a)<BR>\n" );
document.write( "r = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28-12%29%2F%282%2A-1%29 ALIGN=MIDDLE  ALT=\"%28-12%29%2F%282%2A-1%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "r = 6 cm<BR>\n" );
document.write( "Find the max area<BR>\n" );
document.write( "A = -6^2 + 12(6)<BR>\n" );
document.write( "A = -36 + 72<BR>\n" );
document.write( "A = 36 sq cm max area<BR>\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );