document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1044343>Question 1044343</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An inverted regular pyramid whose square base has an area of 16 square units and a height of 6 units contains water with a depth of 3 units. If the said pyramid is set upright, how high is the water level? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #659616 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=659616\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> This problem has numbers and specifications that are not really needed.<BR>\n" );
document.write( "If an inverted pyramid of any shape and size<BR>\n" );
document.write( "is filled with water to half of its height,<BR>\n" );
document.write( "the height of the water after turning it upright is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282-root%283%2C7%29%29%2F2=about0.0435=%224.35%25%22 ALIGN=MIDDLE  ALT=\"%282-root%283%2C7%29%29%2F2=about0.0435=%224.35%25%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the container pyramid's height.<BR>\n" );
document.write( "In the case of a container of height 6 units, originally filled to a depth of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3units=%281%2F2%296units ALIGN=MIDDLE  ALT=\"3units=%281%2F2%296units\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "the final water height is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282-root%283%2C7%29%29%2F2%29%2A6units=%282-root%283%2C7%29%29%2A3units=approximately ALIGN=MIDDLE  ALT=\"%28%282-root%283%2C7%29%29%2F2%29%2A6units=%282-root%283%2C7%29%29%2A3units=approximately\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%280.2612units%29 ALIGN=MIDDLE  ALT=\"highlight%280.2612units%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "The container is a pyramid that has a height <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H=6 ALIGN=MIDDLE  ALT=\"H=6\"   DISABLED_style= \"max-width:90%; height:auto;\" > and a Volume <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V ALIGN=MIDDLE  ALT=\"V\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The part originally filled with water is a similar pyramid.<BR>\n" );
document.write( "Its height is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3=6%2F2=H%2F2=%281%2F2%29H ALIGN=MIDDLE  ALT=\"3=6%2F2=H%2F2=%281%2F2%29H\"   DISABLED_style= \"max-width:90%; height:auto;\" > , half of the height of the container pyramid.<BR>\n" );
document.write( "The original water-filled pyramid is a smaller version of the container pyramid, <BR>\n" );
document.write( "scaled down by a factor of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F2 ALIGN=MIDDLE  ALT=\"1%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "For scaled up or down objects, if the ratio of corresponding length is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the ratio of corresponding volume is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E3 ALIGN=MIDDLE  ALT=\"r%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "If you know one ratio you can find the other.<BR>\n" );
document.write( "So, the volume of that original water-filled pyramid is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F2%29%5E3=1%2F8 ALIGN=MIDDLE  ALT=\"%281%2F2%29%5E3=1%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the volume of the container pyramid.<BR>\n" );
document.write( "When the container pyramid is set upright, the water still fills <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F8 ALIGN=MIDDLE  ALT=\"1%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the volume,<BR>\n" );
document.write( "but now the water is against the base of the container pyramid.<BR>\n" );
document.write( "Above the water there is an air-filled pyramid with volume <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V-%281%2F8%29V=%287%2F8%29V ALIGN=MIDDLE  ALT=\"V-%281%2F8%29V=%287%2F8%29V\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The height of that pyramid is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%2Aroot%283%2C%287%2F8%29%29H=H%2A%28root%283%2C7%29%2F2%29 ALIGN=MIDDLE  ALT=\"H%2Aroot%283%2C%287%2F8%29%29H=H%2A%28root%283%2C7%29%2F2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The height of the water is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H-H%2A%28root%283%2C7%29%2F2%29=H%281-root%283%2C7%29%2F2%29=H%282-root%283%2C7%29%29%2F2 ALIGN=MIDDLE  ALT=\"H-H%2A%28root%283%2C7%29%2F2%29=H%281-root%283%2C7%29%2F2%29=H%282-root%283%2C7%29%29%2F2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );