document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203952>Question 1203952</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Estimate the instantaneous rate of change in the area of a circle when the radius is 3 cm. The formula for the area of a circle is A=πr^2 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #839895 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=839895\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> \r<BR>\n" );
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document.write( "The area of a circle with respect to its radius can be modeled using the following function:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%28r%29+=+pi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"A%28r%29+=+pi%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The derivative of this function is as follows:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > '<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28r%29+=+2pi%2Ar ALIGN=MIDDLE  ALT=\"+%28r%29+=+2pi%2Ar\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Therefore, the instantaneous rate of change of the area of a circle when the radius is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+ ALIGN=MIDDLE  ALT=\"3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >centimeters can be found by calculating <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > ' <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%29 ALIGN=MIDDLE  ALT=\"%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > ' <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283%29+=+2pi%283%29+=+6pi+ ALIGN=MIDDLE  ALT=\"%283%29+=+2pi%283%29+=+6pi+\"   DISABLED_style= \"max-width:90%; height:auto;\" >≈ <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18.85 ALIGN=MIDDLE  ALT=\"18.85\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "We get that the instantaneous rate of change of the area of a circle when the radius is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3+ ALIGN=MIDDLE  ALT=\"3+\"   DISABLED_style= \"max-width:90%; height:auto;\" >centimeters is approximately <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=18.85 ALIGN=MIDDLE  ALT=\"18.85\"   DISABLED_style= \"max-width:90%; height:auto;\" > area square centimeters per radius centimeter.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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