document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=181953>Question 181953</A>: <I><SPAN STYLE=\"word-break: break-all;\">           . Racquetball. The volume of rubber (in cubic centimeters)<BR>\n" );
document.write( "in a hollow rubber ball used in racquetball is given by\r<BR>\n" );
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document.write( " V=4/3 R3^3-4/3 r^3\r<BR>\n" );
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document.write( "where the inside radius is r centimeters and the outside<BR>\n" );
document.write( "radius is R centimeters.<BR>\n" );
document.write( "a) Rewrite the formula by factoring the right-hand side<BR>\n" );
document.write( "completely.<BR>\n" );
document.write( "b) The accompanying graph shows the relationship<BR>\n" );
document.write( "between r and V when R =3. Use the graph to<BR>\n" );
document.write( "estimate the value of r for which V = 100 cm3.\r<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 #136571 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=136571\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Racquetball. The volume of rubber (in cubic centimeters)<BR>\n" );
document.write( "in a hollow rubber ball used in racquetball is given by <BR>\n" );
document.write( "V=4/3 R3^3-4/3 r^3 <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=4%2Api%2AR3%5E3%2F3-4%2Api%2Ar%5E3%2F3 ALIGN=MIDDLE  ALT=\"V=4%2Api%2AR3%5E3%2F3-4%2Api%2Ar%5E3%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > pi was left out<BR>\n" );
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document.write( "where the inside radius is r centimeters and the outside<BR>\n" );
document.write( "radius is R centimeters.<BR>\n" );
document.write( "a) Rewrite the formula by factoring the right-hand side<BR>\n" );
document.write( "completely.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Api%2AR3%5E3%2F3-4%2Api%2Ar%5E3%2F3 ALIGN=MIDDLE  ALT=\"4%2Api%2AR3%5E3%2F3-4%2Api%2Ar%5E3%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2Api%2F3%29%2A%28R%5E3+-+r%5E3%29 ALIGN=MIDDLE  ALT=\"%284%2Api%2F3%29%2A%28R%5E3+-+r%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Factoring this far would be useful.<BR>\n" );
document.write( "=<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2Api%2F3%29%2A%28R-r%29%2A%28R%5E2+%2B+R%2Ar+-+r%5E2%29 ALIGN=MIDDLE  ALT=\"%284%2Api%2F3%29%2A%28R-r%29%2A%28R%5E2+%2B+R%2Ar+-+r%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > There's no advantage to this.<BR>\n" );
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document.write( "b) The accompanying graph shows the relationship<BR>\n" );
document.write( "between r and V when R =3. Use the graph to<BR>\n" );
document.write( "estimate the value of r for which V = 100 cm3.<BR>\n" );
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document.write( "I don't see a graph.<BR>\n" );
document.write( "It says V is the volume of rubber.  100 cc seems like a lot.<BR>\n" );
document.write( "The OD of a ball is 5.7 mm, so R = 2.85 cm<BR>\n" );
document.write( "The total volume of the rubber and the gas inside the ball is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Api%2A2.85%5E3%2F3 ALIGN=MIDDLE  ALT=\"4%2Api%2A2.85%5E3%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "V =~96.967 cc<BR>\n" );
document.write( "Obviously, the composer of the problem now refers to V as the total volume, a lack on consistency.<BR>\n" );
document.write( "To make a graph of this (or anything else) go to www.padowan.dk.com/graph/ and DL the (free) software.\r<BR>\n" );
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