document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=958125>Question 958125</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If the radius of a circular solar cell is increased by a factor of 1.7, the area of the cell increases by 53 <BR>\n" );
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document.write( ". Find the radius (in cm) of the new solar cell.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #585577 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=585577\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The formula for the area of a circle is A = pi * r^2.\r<BR>\n" );
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document.write( "We'll call that A1.\r<BR>\n" );
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document.write( "If the radius is increased by a factor of 1.7, then the new radius is equal to 1.7 * the old radius.\r<BR>\n" );
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document.write( "The formula for this new area becomes A2 = pi * (1.7 * r)^2.\r<BR>\n" );
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document.write( "since the new area is the same as the old area but increased by 53 cm^2, then A2 is equal to A1 + 53 cm^2.\r<BR>\n" );
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document.write( "You get two formulas:\r<BR>\n" );
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document.write( "A1 = pi * r^2\r<BR>\n" );
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document.write( "A1 + 53 = pi * (1.7 * r)^2\r<BR>\n" );
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document.write( "simplify the second equation to get:\r<BR>\n" );
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document.write( "A1 + 53 = pi * 1.7^2 * r^2 which then becomes:\r<BR>\n" );
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document.write( "A1 + 53 = pi * 2.89 * r^2\r<BR>\n" );
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document.write( "your two equations have now become:\r<BR>\n" );
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document.write( "A1 = pi * r^2\r<BR>\n" );
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document.write( "A1 + 53 = pi * r^2 * 2.89\r<BR>\n" );
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document.write( "Subtract the first equation from the second equation to get:\r<BR>\n" );
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document.write( "A1 + 53 - A1 = pi * r^2 * 2.89 - pi * r^2\r<BR>\n" );
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document.write( "simplify this to get:\r<BR>\n" );
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document.write( "53 = pi * r^2 * 1.89\r<BR>\n" );
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document.write( "divide both sides of this equation by 1.89 * pi to get:\r<BR>\n" );
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document.write( "53 / (1.89 * pi) = r^2\r<BR>\n" );
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document.write( "solve for r^2 to get r^2 = 8.926150247\r<BR>\n" );
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document.write( "solve for r to get r = 2.987666355\r<BR>\n" );
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document.write( "That's the length of the original radius.\r<BR>\n" );
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document.write( "Multiply this by 1.7 to get r = 5.079032803\r<BR>\n" );
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document.write( "That's the length of the scaled radius that is 1.7 times as large as the original radius.\r<BR>\n" );
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document.write( "Solve for the respective areas using the respective radii.\r<BR>\n" );
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document.write( "Original radius gets an area of 28.04232804 square cm.\r<BR>\n" );
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document.write( "Enlarged radius gets an area of 81.04232804 square cm.\r<BR>\n" );
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document.write( "The difference is 53.\r<BR>\n" );
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document.write( "this confirms the solution is correct.\r<BR>\n" );
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document.write( "The solution to the question is that the radius of the new solar cell is equal to 5.079032803 cm.\r<BR>\n" );
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