document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205486>Question 1205486</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cone is half full in volume, how deep is the water in the cone if it is 12cm in diameter at the top and the total height of the cone is 16cm.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #842329 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=842329\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The container is a cone; and the water in the container forms a cone that is similar to the whole container.<br><BR>\n" );
document.write( "So there is no need in this problem to bother with the formula for the volume of a cone.  By a powerful general principle for similar figures, if the scale factor (ratio of linear measurements) between two similar figures is A:B, then the ratio of area measurements between the figures is A^2:B^2, and the ratio of volume measurements between the figures is A^3:B^3.<br><BR>\n" );
document.write( "In this problem, the ratio of volumes of the two cones is 1:2, so the ratio of linear measurements is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%3Aroot%283%2C2%29 ALIGN=MIDDLE  ALT=\"1%3Aroot%283%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The height of the large cone (the container) is 16cm, so the height of the small cone (the depth of the water) is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2Froot%283%2C2%29 ALIGN=MIDDLE  ALT=\"16%2Froot%283%2C2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > = 12.70cm to 2 decimal places.<br><BR>\n" );
document.write( "ANSWER: 12.70cm<br><BR>\n" );
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