document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1172158>Question 1172158</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A spherical snowball is melting in such a way that its surface area decreases at the rate of 1 in 2 /min . How fast is its volume shrinking when its radius is 3 in ?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #797124 by </B><A HREF=/tutors/aboutme.mpl?userid=math_helper><B>math_helper(2461)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_helper><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=math_helper><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=797124\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Assuming that \"1 in 2/min\" is supposed to be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+1+%28in%5E2%2Fmin%29+ ALIGN=MIDDLE  ALT=\"+1+%28in%5E2%2Fmin%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=+V+ ALIGN=MIDDLE  ALT=\"+V+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%284%2F3%29pi%2Ar%5E3+ ALIGN=MIDDLE  ALT=\"+%284%2F3%29pi%2Ar%5E3+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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=++4%2Api%2Ar%5E2+ ALIGN=MIDDLE  ALT=\"++4%2Api%2Ar%5E2+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "V in terms of A:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+V+ ALIGN=MIDDLE  ALT=\"+V+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+matrix%283%2C3%2C%22%22%2C%22%22%2C%22%22%2C+%22%22%2C+sqrt%28A%5E3%29%2F%286sqrt%28pi%29%29%2C+%22%22%2C%22%22%2C%22%22%2C%22%22%29+ ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "Taking the derivative of V wrt A:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+dV%2FdA+ ALIGN=MIDDLE  ALT=\"+dV%2FdA+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+sqrt%28A%29%2F%284%2Asqrt%28pi%29%29+ ALIGN=MIDDLE  ALT=\"+sqrt%28A%29%2F%284%2Asqrt%28pi%29%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br>\r<BR>\n" );
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document.write( "Need an expression for dV/dt in terms of information given:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+dV%2Fdt+ ALIGN=MIDDLE  ALT=\"+dV%2Fdt+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%28dV%2FdA%29+%2A+%28dA%2Fdt%29+ ALIGN=MIDDLE  ALT=\"+%28dV%2FdA%29+%2A+%28dA%2Fdt%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <br>\r<BR>\n" );
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document.write( "At r=3, A=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Api%2A3%5E2 ALIGN=MIDDLE  ALT=\"4%2Api%2A3%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36pi ALIGN=MIDDLE  ALT=\"36pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > --->  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28A%29 ALIGN=MIDDLE  ALT=\"sqrt%28A%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+6%2Asqrt%28pi%29+ ALIGN=MIDDLE  ALT=\"+6%2Asqrt%28pi%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "dA/dt is given as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1+%28in%5E2%2Fmin%29+ ALIGN=MIDDLE  ALT=\"1+%28in%5E2%2Fmin%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" > <br>\r<BR>\n" );
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document.write( "So, finally,  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+dV%2Fdt+ ALIGN=MIDDLE  ALT=\"+dV%2Fdt+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+%286%2Asqrt%28pi%29+%2F+%284%2Asqrt%28pi%29%29%29+%2A+1+ ALIGN=MIDDLE  ALT=\"+%286%2Asqrt%28pi%29+%2F+%284%2Asqrt%28pi%29%29%29+%2A+1+\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%283%2F2%29 ALIGN=MIDDLE  ALT=\"highlight%283%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=in%5E3%2Fmin ALIGN=MIDDLE  ALT=\"in%5E3%2Fmin\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Another approach would be to use 'r' instead of 'A':   dV/dt = (dV/dr)*(dr/dt)<BR>\n" );
document.write( "It is about equally messy to go this route.  Because you are given dA/dt, you<BR>\n" );
document.write( " have the additional step dr/dt = (dA/dt)*(dr/dA),  so dV/dt = (dV/dr)*(dA/dt)*(dr/dA) \r<BR>\n" );
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document.write( "Dear student:  Please do not use the \"thank you\" message system to post additional problems.  Please post your questions (one at a time) using<BR>\n" );
document.write( "the normal process.  Thank you.\r<BR>\n" );
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