document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=876802>Question 876802</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi,\r<BR>\n" );
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document.write( "The area of a circle of radius r is given by the formula A=&#960;r^2. Use this fact to find the area for the shaded area in the figure below. \r<BR>\n" );
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document.write( "(The figure is a circle, with radius r, with another shaded circle surrounding it. The shaded part has a width marked 'w'.) \r<BR>\n" );
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document.write( "The answer given is A=2&#960;rw + &#960;w^2. Can you please explain how this is done.\r<BR>\n" );
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document.write( "Thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #529017 by </B><A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><B>josgarithmetic(39617)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josgarithmetic><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=529017\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Examining this part:  (The figure is a circle, with radius r, with another shaded circle surrounding it. The shaded part has a width marked 'w'.) \r<BR>\n" );
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document.write( "The shaded region would be surrounding the unshaded smaller circle.  You want the area for the shaded region.  This will be a difference.  \r<BR>\n" );
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document.write( "Larger circle area, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A%28r%2Bw%29%5E2 ALIGN=MIDDLE  ALT=\"pi%2A%28r%2Bw%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
document.write( "Smaller circle area, <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( "The shaded region should be the larger region minus the small circle region, leaving just the circular shaded region with the width of w.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=pi%28r%2Bw%29%5E2-pi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"A=pi%28r%2Bw%29%5E2-pi%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%28r%5E2%2B2rw%2Bw%5E2%29-pi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"pi%28r%5E2%2B2rw%2Bw%5E2%29-pi%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%28r%5E2%2B2rw%2Bw%5E2-r%5E2%29 ALIGN=MIDDLE  ALT=\"pi%28r%5E2%2B2rw%2Bw%5E2-r%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%282rw%2Bw%5E2%2Br%5E2-r%5E2%29 ALIGN=MIDDLE  ALT=\"pi%282rw%2Bw%5E2%2Br%5E2-r%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%282rw%2Bw%5E2%2B0%29 ALIGN=MIDDLE  ALT=\"pi%282rw%2Bw%5E2%2B0%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A2%2Arw%2Bpi%2Aw%5E2 ALIGN=MIDDLE  ALT=\"pi%2A2%2Arw%2Bpi%2Aw%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >-----which should be clear enough.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2pi%2Arw%2Bpir%5E2 ALIGN=MIDDLE  ALT=\"A=2pi%2Arw%2Bpir%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >---commutative property for multiplication. </SPAN>\n" );
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