document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=160801>Question 160801</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A spherical balloon is being inflated. Estimate the rate at which its surface area is changing with respect to the radius when the radius measures 20 cm.\r<BR>\n" );
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document.write( "Answer: 160pi cm^2/cm<BR>\n" );
document.write( "How do I get it though? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #118565 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=118565\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SA=4%2Api%2AR%5E2 ALIGN=MIDDLE  ALT=\"SA=4%2Api%2AR%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You're looking for the rate of change of SA with respect to R. <BR>\n" );
document.write( "That's the same as the derivative.<BR>\n" );
document.write( "Take a small step in R, calculate the SA, subtract the original SA, and divide by the small step. <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SA%28R%2BdR%29=4%2Api%2A%28R%2BdR%29%5E2=4%2Api%2A%28R%5E2%2B2RdR%2BdR%5E2%29 ALIGN=MIDDLE  ALT=\"SA%28R%2BdR%29=4%2Api%2A%28R%2BdR%29%5E2=4%2Api%2A%28R%5E2%2B2RdR%2BdR%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=SA%28R%29=4%2Api%2AR%5E2 ALIGN=MIDDLE  ALT=\"SA%28R%29=4%2Api%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=%28SA%28R%2BdR%29-S%28R%29%29%2FdR=%284%2Api%2A%28R%5E2%2B2RdR%2BdR%5E2-R%5E2%29%29%2FdR ALIGN=MIDDLE  ALT=\"%28SA%28R%2BdR%29-S%28R%29%29%2FdR=%284%2Api%2A%28R%5E2%2B2RdR%2BdR%5E2-R%5E2%29%29%2FdR\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Assume that <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dR ALIGN=MIDDLE  ALT=\"dR\"   DISABLED_style= \"max-width:90%; height:auto;\" > is small, then <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=dR%5E2 ALIGN=MIDDLE  ALT=\"dR%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is even smaller (=0)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28SA%28R%2BdR%29-S%28R%29%29%2FdR=%284%2Api%2A%282RdR%2Bcross%28dR%5E2%29%29%29%2FdR ALIGN=MIDDLE  ALT=\"%28SA%28R%2BdR%29-S%28R%29%29%2FdR=%284%2Api%2A%282RdR%2Bcross%28dR%5E2%29%29%29%2FdR\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28SA%28R%2BdR%29-S%28R%29%29%2FdR=8%2Api%2AR ALIGN=MIDDLE  ALT=\"%28SA%28R%2BdR%29-S%28R%29%29%2FdR=8%2Api%2AR\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "That's the hard way to find the derivative of SA with respect to R. <BR>\n" );
document.write( "You can also differentiate.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SA=4%2Api%2AR%5E2 ALIGN=MIDDLE  ALT=\"SA=4%2Api%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=d%28SA%29%2FdR=8%2Api%2AR ALIGN=MIDDLE  ALT=\"d%28SA%29%2FdR=8%2Api%2AR\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So when R=20<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d%28SA%29%2FdR=8%2Api%2A20=160%2Api ALIGN=MIDDLE  ALT=\"d%28SA%29%2FdR=8%2Api%2A20=160%2Api\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
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