document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=509424>Question 509424</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A circular pool is surrounded by a brick walkway 3m wide. Find the radius of the pool if the area of the walkway is 198 m^2. \r<BR>\n" );
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document.write( "The walkway is 3 m wide, and A of walkway = 193 m^2....\r<BR>\n" );
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document.write( "I think I need to find the area of the entire circle and subtract the area of the walkway from it, and figure out the radius from there, but I have no idea how to do so. \r<BR>\n" );
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document.write( "I'D LOVE any additional advice on polynomial word problems - rate-time-distance problems, problems involving area... <BR>\n" );
document.write( "Any tips, please??\r<BR>\n" );
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document.write( "Much appreciated! Thank you !! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #341464 by </B><A HREF=/tutors/aboutme.mpl?userid=oberobic><B>oberobic(2304)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=oberobic><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=341464\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The walkway and pool are circular, so the inside circumference of the walkway is less than the outside circumference.  So, you can take the area of the inner circle (which is the pool, actually) and subtract it from the area of the outer circle.<BR>\n" );
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document.write( "pi*r^2 = area of the pool<BR>\n" );
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document.write( "pi*(r+3)^2 = area of the pool + walkway<BR>\n" );
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document.write( "pi*r^2 = pi*(r+3)^2 - 198<BR>\n" );
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document.write( "pi*r^2 = pi*(r^2 +6r +9) - 198<BR>\n" );
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document.write( "pi*r^2 = pi*r^2 + pi*6r + pi*9 -198<BR>\n" );
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document.write( "0 = pi*6r + pi*9 -198<BR>\n" );
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document.write( "pi*6r + pi*9 = 198<BR>\n" );
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document.write( "pi*(6r + 9) = 198<BR>\n" );
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document.write( "6r + 9 = 198/pi = 63.0253575<BR>\n" );
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document.write( "6r = 63.0253575 -9 = 54.0253575<BR>\n" );
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document.write( "r = 54.0253575/6<BR>\n" );
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document.write( "r = 9.00422624<BR>\n" );
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document.write( "r+3 = radius to outer edge of walkway<BR>\n" );
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document.write( "r+3 = 12.00422624<BR>\n" );
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document.write( "inner area = pi*(9.00422624^2)<BR>\n" );
document.write( "inner area = 254.708049<BR>\n" );
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document.write( "outer area = pi*(12.00422624^2)<BR>\n" );
document.write( "outer area = 452.708049<BR>\n" );
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document.write( "walkway area = 452.708049 - 254.708049 = 198<BR>\n" );
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document.write( "Correct.<BR>\n" );
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document.write( "Answer:  The radius of the pool is 9.00422624 or about 9 meters.<BR>\n" );
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document.write( "Done. </SPAN>\n" );
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