document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1083682>Question 1083682</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello,  I have two Similar cones Large and small.  Large cone is 9cm radius 15 cm slant height.  The small cone has a lateral area of 60 pi.<BR>\n" );
document.write( "How do I find the volume of the small cone? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #697710 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=697710\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  \r<BR>\n" );
document.write( "\n" );
document.write( " Large cone is<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=+r%5B1%5D=9cm ALIGN=MIDDLE  ALT=\"+r%5B1%5D=9cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5B1%5D=15cm+ ALIGN=MIDDLE  ALT=\"L%5B1%5D=15cm+\"   DISABLED_style= \"max-width:90%; height:auto;\" > slant height\r<BR>\n" );
document.write( "\n" );
document.write( "small cone has a lateral area of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=LA=60+pi ALIGN=MIDDLE  ALT=\"LA=60+pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "The lateral area of a cone is\r<BR>\n" );
document.write( "\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=LA=pi+%2A+r+%2A+L ALIGN=MIDDLE  ALT=\"LA=pi+%2A+r+%2A+L\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the radius and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L ALIGN=MIDDLE  ALT=\"L\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the slant height\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60pi=pi+%2A+r+%2A+L ALIGN=MIDDLE  ALT=\"60pi=pi+%2A+r+%2A+L\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60=+r+%2A+L ALIGN=MIDDLE  ALT=\"60=+r+%2A+L\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2FL=+r+ ALIGN=MIDDLE  ALT=\"60%2FL=+r+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "since cones similar, radii and  slant heights are proportional:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5B1%5D%2Fr=L%5B1%5D%2FL ALIGN=MIDDLE  ALT=\"r%5B1%5D%2Fr=L%5B1%5D%2FL\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9%2F%2860%2FL%29=15%2FL ALIGN=MIDDLE  ALT=\"9%2F%2860%2FL%29=15%2FL\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9L%2F60=15%2FL ALIGN=MIDDLE  ALT=\"9L%2F60=15%2FL\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3L%2F20=15%2FL ALIGN=MIDDLE  ALT=\"3L%2F20=15%2FL\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3L%2AL=15%2A20 ALIGN=MIDDLE  ALT=\"3L%2AL=15%2A20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2=%2815%2A20%29%2F3 ALIGN=MIDDLE  ALT=\"L%5E2=%2815%2A20%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2=5%2A20 ALIGN=MIDDLE  ALT=\"L%5E2=5%2A20\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5E2=100 ALIGN=MIDDLE  ALT=\"L%5E2=100\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L=10cm ALIGN=MIDDLE  ALT=\"L=10cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >->  slant height of a small cone\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2FL=+r+ ALIGN=MIDDLE  ALT=\"60%2FL=+r+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60%2F10cm=+r+ ALIGN=MIDDLE  ALT=\"60%2F10cm=+r+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6cm=+r+ ALIGN=MIDDLE  ALT=\"6cm=+r+\"   DISABLED_style= \"max-width:90%; height:auto;\" >-> radius of  a small cone\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "now we can find a volume:\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=%281%2F3%29b%2Ah ALIGN=MIDDLE  ALT=\"V=%281%2F3%29b%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" > where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > is base and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > height of the cone\r<BR>\n" );
document.write( "\n" );
document.write( "base is a circle: area is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2pi ALIGN=MIDDLE  ALT=\"r%5E2pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=%281%2F3%29r%5E2%2Api%2Ah ALIGN=MIDDLE  ALT=\"V=%281%2F3%29r%5E2%2Api%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "we will find height using Pythagorean theorem: \r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2=L%5E2-r%5E2 ALIGN=MIDDLE  ALT=\"h%5E2=L%5E2-r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > -><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=sqrt%2810%5E2-6%5E2%29 ALIGN=MIDDLE  ALT=\"h=sqrt%2810%5E2-6%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > -><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=sqrt%28100-36%29 ALIGN=MIDDLE  ALT=\"h=sqrt%28100-36%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=sqrt%2864%29 ALIGN=MIDDLE  ALT=\"h=sqrt%2864%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >-><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=8cm ALIGN=MIDDLE  ALT=\"h=8cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=%281%2F3%29%286cm%29%5E2%2Api%2A8cm ALIGN=MIDDLE  ALT=\"V=%281%2F3%29%286cm%29%5E2%2Api%2A8cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=%281%2Fcross%283%29%29%28cross%2836%2912cm%5E2%2Api%2A8cm%29 ALIGN=MIDDLE  ALT=\"V=%281%2Fcross%283%29%29%28cross%2836%2912cm%5E2%2Api%2A8cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=12cm%5E2%2Api%2A8cm ALIGN=MIDDLE  ALT=\"V=12cm%5E2%2Api%2A8cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=96cm%5E3%2Api ALIGN=MIDDLE  ALT=\"V=96cm%5E3%2Api\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );