document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151760>Question 1151760</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The two right circular cones are similar. The height of the larger cone is 80 cm, and the area of its base is 3675 cm squared. The area of the base of the smaller cone is 147 Cm squared. What is the volume of the smaller cone? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #773605 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=773605\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> One dimensional measurements (side lengths, perimeters, etc.) are in the ratio <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%3Ab ALIGN=MIDDLE  ALT=\"a%3Ab\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "Two dimensional measurements (area, surface area, etc.) are in the ratio of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E2%3Ab%5E2 ALIGN=MIDDLE  ALT=\"a%5E2%3Ab%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Three dimensional measurements (volume) are in the ratio of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3%3Ab%5E3 ALIGN=MIDDLE  ALT=\"a%5E3%3Ab%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "The ratio of the smaller area to the larger area is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=147%2F3675=1%2F25 ALIGN=MIDDLE  ALT=\"147%2F3675=1%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then. the ratio of the height of the smaller cone and height of the larger cone<BR>\n" );
document.write( " (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80cm ALIGN=MIDDLE  ALT=\"80cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > )is \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2F80=sqrt%281%2F25%29=1%2F5 ALIGN=MIDDLE  ALT=\"h%2F80=sqrt%281%2F25%29=1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" > => <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=16cm ALIGN=MIDDLE  ALT=\"h=16cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, ratio of the heights is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5Bs%5D%2Fh%5Bl%5D=1%2F5 ALIGN=MIDDLE  ALT=\"h%5Bs%5D%2Fh%5Bl%5D=1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "then, volumes are in the ratio of \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3%2Fb%5E3=%281%2F5%29%5E3 ALIGN=MIDDLE  ALT=\"a%5E3%2Fb%5E3=%281%2F5%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3%2Fb%5E3=1%2F125 ALIGN=MIDDLE  ALT=\"a%5E3%2Fb%5E3=1%2F125\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%5E3%2Fb%5E3=0.008 ALIGN=MIDDLE  ALT=\"a%5E3%2Fb%5E3=0.008\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "using formula for the area of a smaller cone, we calculate radius: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=++pi%2Ar%28r+%2B+sqrt%28r%5E2+%2B+16%5E2%29%29 ALIGN=MIDDLE  ALT=\"A=++pi%2Ar%28r+%2B+sqrt%28r%5E2+%2B+16%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=147=++3.14%2Ar%28r+%2B+sqrt%28r%5E2+%2B16%5E2%29%29 ALIGN=MIDDLE  ALT=\"147=++3.14%2Ar%28r+%2B+sqrt%28r%5E2+%2B16%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=2.5cm ALIGN=MIDDLE  ALT=\"r=2.5cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "using formula for the area of a larger cone, we calculate radius:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=++pi%2Ar%28r+%2B+sqrt%28r%5E2+%2B+h%5E2%29%29 ALIGN=MIDDLE  ALT=\"A+=++pi%2Ar%28r+%2B+sqrt%28r%5E2+%2B+h%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3675=++pi%2Ar%28r+%2B+sqrt%28r%5E2+%2B+80%5E2%29%29 ALIGN=MIDDLE  ALT=\"3675=++pi%2Ar%28r+%2B+sqrt%28r%5E2+%2B+80%5E2%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=12.5cm ALIGN=MIDDLE  ALT=\"r=12.5cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the volume of a smaller cone is: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+%281%2F3%29pi%2Ar%5E2%2Ah ALIGN=MIDDLE  ALT=\"V+=+%281%2F3%29pi%2Ar%5E2%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+%281%2F3%29pi%2A%282.5%29%5E2%2A16 ALIGN=MIDDLE  ALT=\"V+=+%281%2F3%29pi%2A%282.5%29%5E2%2A16\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28V=104.72cm%5E3%29 ALIGN=MIDDLE  ALT=\"highlight%28V=104.72cm%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "the volume of a larger cone is: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+%281%2F3%29pi%2Ar%5E2%2Ah ALIGN=MIDDLE  ALT=\"V+=+%281%2F3%29pi%2Ar%5E2%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" >=><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+%281%2F3%29pi%2A%2812.5%29%5E2%2A80=13089.97cm%5E3 ALIGN=MIDDLE  ALT=\"V+=+%281%2F3%29pi%2A%2812.5%29%5E2%2A80=13089.97cm%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "check the ratio:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=104.72%2F13089.97+=0.008 ALIGN=MIDDLE  ALT=\"104.72%2F13089.97+=0.008\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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