document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=292216>Question 292216</A>: <I><SPAN STYLE=\"word-break: break-all;\"> As sand is poured from a chute, it forms a right circular cone whose height is one-fourth of the radius of the base. What is the radius of the base when the cone has a volume of 144 cubic feet? You may use the formula V=1/3(pi)r^2h for the volume of a right circular cone with a radius r and height h.<BR>\n" );
document.write( "Hope this is the correct section to post this question.<BR>\n" );
document.write( "I have no idea how to solve this problem and don't understand that formula. Could somebody please explain how to solve this, or at least show me the steps so I can figure it out from there?<BR>\n" );
document.write( "Thanks! Any help is appreciated. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #211293 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=211293\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> As sand is poured from a chute, it forms a right circular cone whose height is<BR>\n" );
document.write( " one-fourth of the radius of the base.<BR>\n" );
document.write( " What is the radius of the base when the cone has a volume of 144 cubic feet?<BR>\n" );
document.write( " You may use the formula V=1/3(pi)r^2h for the volume of a right circular<BR>\n" );
document.write( " cone with a radius r and height h.<BR>\n" );
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document.write( "Note that the volume of a cone is 1/3 the volume of a cylinder<BR>\n" );
document.write( "r = radius, h = height<BR>\n" );
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document.write( "They give you the volume so we have:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%2Api%2Ar%5E2%2Ah ALIGN=MIDDLE  ALT=\"%281%2F3%29%2Api%2Ar%5E2%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 144<BR>\n" );
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document.write( "It says,\"height is one-fourth of the radius of the base.: therefore<BR>\n" );
document.write( "h = .25r<BR>\n" );
document.write( "replacing h with .25r in the formula we have<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%2Api%2Ar%5E2%2A.25r ALIGN=MIDDLE  ALT=\"%281%2F3%29%2Api%2Ar%5E2%2A.25r\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 144<BR>\n" );
document.write( "Now we only have one unknown, r<BR>\n" );
document.write( "Multiply both sides by 3 to get rid of the fraction<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ar%5E2%2A.25r ALIGN=MIDDLE  ALT=\"pi%2Ar%5E2%2A.25r\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 3(144)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ar%5E2%2A.25r ALIGN=MIDDLE  ALT=\"pi%2Ar%5E2%2A.25r\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 432<BR>\n" );
document.write( "Which is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A.25r%5E3 ALIGN=MIDDLE  ALT=\"pi%2A.25r%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 432<BR>\n" );
document.write( "divide both sides by pi<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.25r%5E3 ALIGN=MIDDLE  ALT=\".25r%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=432%2Fpi ALIGN=MIDDLE  ALT=\"432%2Fpi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=.25r%5E3 ALIGN=MIDDLE  ALT=\".25r%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 137.5<BR>\n" );
document.write( "Multiply both sides by 4 to get rid of .25<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E3 ALIGN=MIDDLE  ALT=\"r%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 4(137.5)<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E3 ALIGN=MIDDLE  ALT=\"r%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 550<BR>\n" );
document.write( "r = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=550%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"550%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the cube root of both sides<BR>\n" );
document.write( "use a calc, enter 550^(1/3)<BR>\n" );
document.write( "r = 8.2 ft is the radius<BR>\n" );
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document.write( "See if that is right<BR>\n" );
document.write( "r = 8.2, h = .25(8.2) = 2.05<BR>\n" );
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document.write( "v = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%2Api%2A8.2%5E2%2A2.05 ALIGN=MIDDLE  ALT=\"%281%2F3%29%2Api%2A8.2%5E2%2A2.05\"   DISABLED_style= \"max-width:90%; height:auto;\" > <BR>\n" );
document.write( "v = 144.3 close enough to confirm our solution of r = 8.2<BR>\n" );
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document.write( "Did this help you understand this problem?<BR>\n" );
document.write( " </SPAN>\n" );
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