document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=256825>Question 256825</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The formula relating the volume, V, of a baloon and its radius,r, as it is being inflated is: V(r)=4/3 pi r^3,where r is the radius in cm.\r<BR>\n" );
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document.write( "a) Determine the average rate of change in volume between r=2 and r=10cm.<BR>\n" );
document.write( "b) Determine the average rate of change in volume between r=8 and r=10cm.<BR>\n" );
document.write( "c) Determine the average rate of change in volume between r=9.99 and r=10<BR>\n" );
document.write( "d) Calculate the value of 4 pi r ^2 for r=10. What do you notice? <BR>\n" );
document.write( "Please help me :) Thanks. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #188875 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=188875\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The formula relating the volume, V, of a baloon and its radius,r, as it is being inflated is: V(r)=4/3 pi r^3,where r is the radius in cm. <BR>\n" );
document.write( "a) Determine the average rate of change in volume between r=2 and r=10cm.<BR>\n" );
document.write( "At r=2, Vol = (32/3) pi cc =~ 33.51 cc<BR>\n" );
document.write( "At r=10, Vol = (4000/3)pi cc =~4188.79 cc<BR>\n" );
document.write( "Diff = (3968/3)pi cc<BR>\n" );
document.write( "Avg rate of change = (3968/3)*pi/(10-2) =~ 519.41<BR>\n" );
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document.write( "b) Determine the average rate of change in volume between r=8 and r=10cm.<BR>\n" );
document.write( "At r=8, Vol = (2048/3)pi cc =~ 2144.66 cc<BR>\n" );
document.write( "At r=10, Vol = (4000/3)pi cc =~ 4188.79 cc<BR>\n" );
document.write( "Avg rate of change = (1952*pi/3)/(10-8) = ~ 1022<BR>\n" );
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document.write( "c) Determine the average rate of change in volume between r=9.99 and r=10<BR>\n" );
document.write( "At r = 9.99, Vol =~ 4176.24 cc<BR>\n" );
document.write( "At r = 10, Vol =~ 4188.79 cc<BR>\n" );
document.write( "Avg rate of change =~ 1255<BR>\n" );
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document.write( "d) Calculate the value of 4 pi r ^2 for r=10. What do you notice? <BR>\n" );
document.write( "4pi*r^2 = 4000pi =~ 1256.637<BR>\n" );
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document.write( "As the difference between 10 and the other radius becomes smaller, the average rate of change becomes closer to 4pi*r^2 at r=10.<BR>\n" );
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document.write( "Tho it might not be relevant, 4pi*r^2 is the surface area of the sphere.<BR>\n" );
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document.write( "PS  I did these on a calculator, but I recommend using Excel.  Errors are less likely, and you can easily change the increments and see the effects.\r<BR>\n" );
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