document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1193372>Question 1193372</A>: <I><SPAN STYLE=\"word-break: break-all;\"> At what distance from the base of a right circular cone must a plane be passed parallel to the base in order that the volume of the frustum formed shall be three-fifths of the volume of the given cone?\r<BR>\n" );
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document.write( "Pls. if anyone can help me? I try the volume of the frustum formula but I still didn't get it but I know that the answer is 0.26319h. Hope anyone could notice me. Thank you very much. More power! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #825378 by </B><A HREF=/tutors/aboutme.mpl?userid=greenestamps><B>greenestamps(13200)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=greenestamps><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=greenestamps><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=825378\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The nice thing about this problem is that you don't need to deal with the formula for the volume of a frustum, or with ANY geometric formula.<br><BR>\n" );
document.write( "If the volume of the frustum is 3/5 of the volume of the whole cone, then the small cone that is cut off by the plane is 2/5 of the volume of the whole cone.<br><BR>\n" );
document.write( "The two cones are similar, so the ratio of the volumes is the cube of the ratio of the heights.  Knowing that the volume of the small cone is 2/5 of the volume of the whole cone, the ratio of the heights of the two cones is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F5%29%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"%282%2F5%29%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 0.73681 to 5 decimal places.<br><BR>\n" );
document.write( "Then, since the height of the small cone is 0.73681 times the height of the whole cone, the height of the frustum is 1-0.73681 = 0.26319 times the height of the whole cone.<br><BR>\n" );
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document.write( "Clarification for the student who asked a question about my response....<br><BR>\n" );
document.write( "The ratio of the volumes is the cube (3rd power) of the ratio of the heights; so the ratio of the heights is the CUBE ROOT (1/3 power) of the ratio of the volumes.<br><BR>\n" );
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document.write( "NO!!!<br><BR>\n" );
document.write( "The problem has nothing to do with the formula for the volume of a cone (which happens to contain a factor of 1/3).<br><BR>\n" );
document.write( "The 1/3 in the problem is an exponent.  The ratio of heights of the two cones is the cube root (1/3 power) of the ratio of the volumes.<br><BR>\n" );
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