document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=265854>Question 265854</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Tony needs a glass bell jar in the shape of a cylinder with a hemisphere on top. The height of the cylinder must be 3 inches longer than its radius and the volume must be 72pi cubic inches. What should the radius of the cylinder be?\r<BR>\n" );
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document.write( "The name of the lesson is Fundamental Theorem of Algebra.<BR>\n" );
document.write( "Do i need to find the roots to get the radius? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #195605 by </B><A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><B>ankor@dixie-net.com(22740)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ankor@dixie-net.com><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=ankor@dixie-net.com><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=195605\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Tony needs a glass bell jar in the shape of a cylinder with a hemisphere on top. The height of the cylinder must be 3 inches longer than its radius and the volume must be 72pi cubic inches. What should the radius of the cylinder be?<BR>\n" );
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document.write( "Let r = the radius of the cylinder (and the hemisphere)<BR>\n" );
document.write( "then<BR>\n" );
document.write( "(r+3) = the height of the cylinder<BR>\n" );
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document.write( "vol of a sphere =<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;\" >, therefore<BR>\n" );
document.write( "vol of a hemisphere = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29pi%2Ar%5E3 ALIGN=MIDDLE  ALT=\"%282%2F3%29pi%2Ar%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "vol of cylinder + vol of hemisphere = 72*pi<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ar%5E2%2Ah ALIGN=MIDDLE  ALT=\"pi%2Ar%5E2%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29pi%2Ar%5E3 ALIGN=MIDDLE  ALT=\"%282%2F3%29pi%2Ar%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=72pi ALIGN=MIDDLE  ALT=\"72pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Divide thru by pi and eliminate that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2%2Ah ALIGN=MIDDLE  ALT=\"r%5E2%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29%28r%5E3%29 ALIGN=MIDDLE  ALT=\"%282%2F3%29%28r%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 72<BR>\n" );
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document.write( "Replace h with (r+3) <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2%2A%28r%2B3%29 ALIGN=MIDDLE  ALT=\"r%5E2%2A%28r%2B3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29r%5E3 ALIGN=MIDDLE  ALT=\"%282%2F3%29r%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 72<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E3%2B3r%5E2%29 ALIGN=MIDDLE  ALT=\"r%5E3%2B3r%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29r%5E3 ALIGN=MIDDLE  ALT=\"%282%2F3%29r%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 72<BR>\n" );
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document.write( "Add like terms r^3 + 2/3*r^3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F3%29%28r%5E3%29 ALIGN=MIDDLE  ALT=\"%285%2F3%29%28r%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > + <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3r%5E2 ALIGN=MIDDLE  ALT=\"3r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 72<BR>\n" );
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document.write( "Multiply each term by 3<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5r%5E3+%2B+9r%5E2 ALIGN=MIDDLE  ALT=\"5r%5E3+%2B+9r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 216<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5r%5E3+%2B+9r%5E2+-+216 ALIGN=MIDDLE  ALT=\"5r%5E3+%2B+9r%5E2+-+216\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0<BR>\n" );
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document.write( "Graph this equation, find x intercept<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+graph%28+300%2C+200%2C+-4%2C+10%2C+-100%2C+300%2C+5x%5E3%2B9x%5E2-216%29+ ALIGN=MIDDLE  ALT=\"+graph%28+300%2C+200%2C+-4%2C+10%2C+-100%2C+300%2C+5x%5E3%2B9x%5E2-216%29+\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "r = 3 inches the radius<BR>\n" );
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document.write( "Check; find the volumes<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A3%5E2%2A6 ALIGN=MIDDLE  ALT=\"pi%2A3%5E2%2A6\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 169.646<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29pi%2A3%5E3 ALIGN=MIDDLE  ALT=\"%282%2F3%29pi%2A3%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 56.487<BR>\n" );
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document.write( "Total volume is 226.195 divide this by pi you have 71.999 ~ 72<BR>\n" );
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