document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=822729>Question 822729</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Figure 1 represents a conical container with a diameter of 120cm and a depth of 140cm. It is filled with water to a depth of 60cm.<BR>\n" );
document.write( "a) Find the volume of water in the container. (SOLVED)<BR>\n" );
document.write( "b) Find the surface area of container in contact with the water. (SOLVED) <BR>\n" );
document.write( "c)The container in Fig. 1 is inverted so that the water is now at the base of the cone with height h cm. Calculate the value of h. <BR>\n" );
document.write( "* Fig. 1's cone is inverted with the tip facing down , fig<BR>\n" );
document.write( " 2's cone is the upright one with th base on the ground.\r<BR>\n" );
document.write( "\n" );
document.write( "Appreciate your help as this is the last question for my holiday assignment. Thanks ! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #495127 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=495127\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The volume of a cone can be calculated as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2AR%5E2%2AH%2F3 ALIGN=MIDDLE  ALT=\"pi%2AR%5E2%2AH%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the radius of the base and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H ALIGN=MIDDLE  ALT=\"H\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the height of the cone.<BR>\n" );
document.write( "Inside that conical container,<BR>\n" );
document.write( "there is a cone of water at first,<BR>\n" );
document.write( "with air above it.<BR>\n" );
document.write( "When the container is inverted,<BR>\n" );
document.write( "there is a cone of air on top,<BR>\n" );
document.write( "and water below it.<BR>\n" );
document.write( "All the cones are similar.<BR>\n" );
document.write( "The radius of the conical container, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=120cm%2F2=60cm ALIGN=MIDDLE  ALT=\"120cm%2F2=60cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=60cm%2F%22140+cm%22=3%2F7 ALIGN=MIDDLE  ALT=\"60cm%2F%22140+cm%22=3%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > of the height.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%2FH=3%2F7 ALIGN=MIDDLE  ALT=\"R%2FH=3%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > <---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R=3H%2F7 ALIGN=MIDDLE  ALT=\"R=3H%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The ratio is the same for all the other similar cones.<BR>\n" );
document.write( "Their volume is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%2Api%2AR%5E2%2AH=%281%2F3%29%2Api%2A%283H%2F7%29%5E2%2AH=%281%2F3%29%2Api%2A%289H%5E2%2F49%29%2AH=pi%2A3%2AH%5E3%2F49 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The volume of the conical container, in cubic centimeters, is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A3%2A140%5E3%2F49=168000pi=about527788 ALIGN=MIDDLE  ALT=\"pi%2A3%2A140%5E3%2F49=168000pi=about527788\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The volume of water in the container, in cubic centimeters, is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A3%2A60%5E3%2F49=648000pi%2F49=about41546 ALIGN=MIDDLE  ALT=\"pi%2A3%2A60%5E3%2F49=648000pi%2F49=about41546\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The volume of air in the container, in cubic centimeters, is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=168000pi-648000pi%2F49=7584000pi%2F49=about486242 ALIGN=MIDDLE  ALT=\"168000pi-648000pi%2F49=7584000pi%2F49=about486242\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "We can find the height, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H ALIGN=MIDDLE  ALT=\"H\"   DISABLED_style= \"max-width:90%; height:auto;\" >, of the cone of air, in cm:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A3%2AH%5E3%2F49=7584000pi%2F49 ALIGN=MIDDLE  ALT=\"pi%2A3%2AH%5E3%2F49=7584000pi%2F49\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3%2AH%5E3=7584000 ALIGN=MIDDLE  ALT=\"3%2AH%5E3=7584000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%5E3=7584000%2F3 ALIGN=MIDDLE  ALT=\"H%5E3=7584000%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H%5E3=2528000 ALIGN=MIDDLE  ALT=\"H%5E3=2528000\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=H=root%283%2C2528000%29=about136.2 ALIGN=MIDDLE  ALT=\"H=root%283%2C2528000%29=about136.2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Once the cone is standing on its base, there is a cone of air inside the tip of the container that has a height of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=136.2cm ALIGN=MIDDLE  ALT=\"136.2cm\"   DISABLED_style= \"max-width:90%; height:auto;\" >  .<BR>\n" );
document.write( "If <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=136.2cm ALIGN=MIDDLE  ALT=\"136.2cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > at the tip of the cone are air, the remaining <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28h=3.8cm%29 ALIGN=MIDDLE  ALT=\"highlight%28h=3.8cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > at the base of the cone are full of water.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=140cm-136.2cm=3.8cm ALIGN=MIDDLE  ALT=\"140cm-136.2cm=3.8cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );