document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=872900>Question 872900</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A solid cone, C, is cut into two parts, X (upper) and Y (lower) by a plane parallel to the base. The lengths od the sloping edges of X is 3 cm, and Y is 2 cm. Find the ratio of:<BR>\n" );
document.write( "a) The diameter of the base of X and C<BR>\n" );
document.write( "b) the area of the bases of X and C<BR>\n" );
document.write( "c) the volume of X and Y\r<BR>\n" );
document.write( "\n" );
document.write( "I tried to use the formula for calculating thr volume of a cone: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%2A3.14%2Ar%5E2%2Ah ALIGN=MIDDLE  ALT=\"%281%2F3%29%2A3.14%2Ar%5E2%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" > but I don't know how to apply it in this question. I also know that I have to use the formula: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A1%2FA2+=+%28l1%2Fl2%29%5E2 ALIGN=MIDDLE  ALT=\"A1%2FA2+=+%28l1%2Fl2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A1%2FA2+=+%28l1%2Fl2%29%5E3 ALIGN=MIDDLE  ALT=\"A1%2FA2+=+%28l1%2Fl2%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #526526 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=526526\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If two figures (on a plane), or two solid 3D shapes are similar (same shape, but maybe scaled up or down), the ratio of a certain length measures <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L ALIGN=MIDDLE  ALT=\"L\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the ratios of surface areas <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > and volumes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V ALIGN=MIDDLE  ALT=\"V\"   DISABLED_style= \"max-width:90%; height:auto;\" > are related.<BR>\n" );
document.write( "Those relations are simple to understand; it's not rocket science.<BR>\n" );
document.write( "Since scaling up (or down) is multiplying every length measurement by the same factor, that factor will be the ratio of the measures of any specific length.<BR>\n" );
document.write( "So for any specific length measured (height, diameter, sloping edge, etc), the ratio is the scaling factor and is always the same.<BR>\n" );
document.write( "Each surface area are the product of two lengths, so the ratios of specific surface areas will be the scaling factor, squared.<BR>\n" );
document.write( "The volumes are the product of 3 lengths, and so their ratio is the scaling factor, cubed.<BR>\n" );
document.write( "Those logically derived, simple relations can be expressed as mathematical formulas (equations) that can sound impressive:<BR>\n" );
document.write( "As for areas and volumes:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A1%2FA2=%28L1%2FL2%29%5E2 ALIGN=MIDDLE  ALT=\"A1%2FA2=%28L1%2FL2%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V1%2FV2=%28L1%2FL2%29%5E3 ALIGN=MIDDLE  ALT=\"V1%2FV2=%28L1%2FL2%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "For other length, if we know length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L ALIGN=MIDDLE  ALT=\"L\"   DISABLED_style= \"max-width:90%; height:auto;\" > for the two similar figured or solids,<BR>\n" );
document.write( "the ratio of the measures of another length, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D ALIGN=MIDDLE  ALT=\"D\"   DISABLED_style= \"max-width:90%; height:auto;\" > on the same figures or solids would also be the same scaling factor used for length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L ALIGN=MIDDLE  ALT=\"L\"   DISABLED_style= \"max-width:90%; height:auto;\" > so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5B1%5D%2FD%5B2%5D=L%5B1%5D%2FL%5B2%5D ALIGN=MIDDLE  ALT=\"D%5B1%5D%2FD%5B2%5D=L%5B1%5D%2FL%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "That is what you were trying to state, isn't it?<BR>\n" );
document.write( "You are on the right track, so I will give you the needed little nudge forward.<BR>\n" );
document.write( " <BR>\n" );
document.write( "The original cone (C) had a sloping edge measuring<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5BC%5D=3cm%2B2cm=5cm ALIGN=MIDDLE  ALT=\"L%5BC%5D=3cm%2B2cm=5cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "That original cone (C) is similar to the upper piece (X), which has a sloping edge measuring<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=L%5BX%5D=3cm ALIGN=MIDDLE  ALT=\"L%5BX%5D=3cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Since cone X (the upper piece) is similar to cone C (the original cone), you can use the ratios and relations above.<BR>\n" );
document.write( " <BR>\n" );
document.write( "a) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=D%5BX%5D%2FD%5BC%5D=L%5BX%5D%2FL%5BC%5D=highlight%283%2F5%29 ALIGN=MIDDLE  ALT=\"D%5BX%5D%2FD%5BC%5D=L%5BX%5D%2FL%5BC%5D=highlight%283%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "b) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A%5BX%5D%2FA%5BC%5D=%28LX%2FLC%29%5E2=%283%2F5%29%5E2=highlight%289%2F15%29 ALIGN=MIDDLE  ALT=\"A%5BX%5D%2FA%5BC%5D=%28LX%2FLC%29%5E2=%283%2F5%29%5E2=highlight%289%2F15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " <BR>\n" );
document.write( "c) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5BX%5D%2FV%5BC%5D=%28LX%2FLC%29%5E3=%283%2F5%29%5E3=27%2F125 ALIGN=MIDDLE  ALT=\"V%5BX%5D%2FV%5BC%5D=%28LX%2FLC%29%5E3=%283%2F5%29%5E3=27%2F125\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Then,<BR>\n" );
document.write( " <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5BX%5D%2FV%5BC%5D=27%2F125 ALIGN=MIDDLE  ALT=\"V%5BX%5D%2FV%5BC%5D=27%2F125\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5BX%5D=%2827%2F125%29V%5BC%5D ALIGN=MIDDLE  ALT=\"V%5BX%5D=%2827%2F125%29V%5BC%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and since we know that<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5BX%5D%2BV%5BY%5D=V%5BC%5D ALIGN=MIDDLE  ALT=\"V%5BX%5D%2BV%5BY%5D=V%5BC%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><---><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5BY%5D=V%5BC%5D-V%5BX%5D ALIGN=MIDDLE  ALT=\"V%5BY%5D=V%5BC%5D-V%5BX%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > , so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5BY%5D=V%5BC%5D-%2827%2F125%29V%5BC%5D ALIGN=MIDDLE  ALT=\"V%5BY%5D=V%5BC%5D-%2827%2F125%29V%5BC%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5BY%5D=%281-27%2F125%29V%5BC%5D ALIGN=MIDDLE  ALT=\"V%5BY%5D=%281-27%2F125%29V%5BC%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5BY%5D=%28125%2F125-27%2F125%29V%5BC%5D ALIGN=MIDDLE  ALT=\"V%5BY%5D=%28125%2F125-27%2F125%29V%5BC%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5BY%5D=%28%28125-27%29%2F125%29V%5BC%5D ALIGN=MIDDLE  ALT=\"V%5BY%5D=%28%28125-27%29%2F125%29V%5BC%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5BY%5D=%2898%2F125%29V%5BC%5D ALIGN=MIDDLE  ALT=\"V%5BY%5D=%2898%2F125%29V%5BC%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5BX%5D%2FV%5BY%5D=%2827%2F125%29V%5BC%5D%2F%28%2898%2F125%29V%5BC%5D%29 ALIGN=MIDDLE  ALT=\"V%5BX%5D%2FV%5BY%5D=%2827%2F125%29V%5BC%5D%2F%28%2898%2F125%29V%5BC%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5BX%5D%2FV%5BY%5D=%28%2827%2F125%29%29%2F%28%2898%2F125%29%29=%2827%2F125%29%28125%2F98%29=highlight%2827%2F98%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );