document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=575067>Question 575067</A>: <I><SPAN STYLE=\"word-break: break-all;\"> An inverted square pyramid has a height equal to 8 meters and a top edge to 3 meters. Initially, it contains water to the depth of 5 meters.<BR>\n" );
document.write( " a. What is the initial volume of the water in the tank?<BR>\n" );
document.write( " b. If the additional water is to be pumped into the tank at the rate of 20 gallons per minute, how many hours will it take to fill the tank? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #369455 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=369455\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> For a square base pyramid<BR>\n" );
document.write( "s=length of base side (in meters)<BR>\n" );
document.write( "h=height (in meters<BR>\n" );
document.write( "V=volume (in cubic meters<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=%281%2F3%29s%5E2%2Ah ALIGN=MIDDLE  ALT=\"V=%281%2F3%29s%5E2%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The inverted pyramid tank has A volume of<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=%281%2F3%293%5E2%2A8=%281%2F3%29%2A9%2A8=24 ALIGN=MIDDLE  ALT=\"V=%281%2F3%293%5E2%2A8=%281%2F3%29%2A9%2A8=24\"   DISABLED_style= \"max-width:90%; height:auto;\" > cubic meters<BR>\n" );
document.write( "a. The initial volume of water in the tank is the volume of a similar pyramid with<BR>\n" );
document.write( "a height of 5 meters. Since the this pyramid and the 8 meter high pyramid are similar, with a height ratio of<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5%2F8 ALIGN=MIDDLE  ALT=\"5%2F8\"   DISABLED_style= \"max-width:90%; height:auto;\" >, the ratio of their volumes is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F8%29%5E3 ALIGN=MIDDLE  ALT=\"%285%2F8%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So the initial volume of water in the tank is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F8%29%5E3%2A24=75%2F64=5.859375 ALIGN=MIDDLE  ALT=\"%285%2F8%29%5E3%2A24=75%2F64=5.859375\"   DISABLED_style= \"max-width:90%; height:auto;\" > cubic meters<BR>\n" );
document.write( "b.Since the tank's volume was 24 cubic meters, the amount of water that must be added to fill the tank (in cubic meters) is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=24-75%2F64=24-5.859375=18.140625 ALIGN=MIDDLE  ALT=\"24-75%2F64=24-5.859375=18.140625\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "One cubic meter is 1000 liters and one US gallon is approximately 3.79L, so we approximate and convert<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2818.14m%5E3%29%281000L%2Fm%5E3%29%281gallon%2F3.79L%29 ALIGN=MIDDLE  ALT=\"%2818.14m%5E3%29%281000L%2Fm%5E3%29%281gallon%2F3.79L%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >=approximately 4786 gallons<BR>\n" );
document.write( "At 20 gallons per minute, with 60 minutes per hour, the hours needed to fill the tank are<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284786gallons%29%281minute%2F20gallons%29%281hour%2F60minutes%29 ALIGN=MIDDLE  ALT=\"%284786gallons%29%281minute%2F20gallons%29%281hour%2F60minutes%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >= approximately 3.99hours, so we'll say that thew answer is 4 hours. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );