document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1136735>Question 1136735</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A right circular cylinder of height 12cm and radius 4cm is filled with water. A heavy circular cone of height 9cm and base radius 6cm is lowered, with vertex downwards and axis vertical, into the cylinder until the cone rests on the rim of the cylinder. Find the<BR>\n" );
document.write( "1. volume of water which spills over from the cylinder, and<BR>\n" );
document.write( "2. height of the water in the cylinder after the cone has been removed. </SPAN>\n" );
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document.write( "The volume of the cylinder is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28pi%29%28r%5E2%29%28h%29+=+%28pi%29%284%5E2%29%2812%29+=+192%28pi%29 ALIGN=MIDDLE  ALT=\"%28pi%29%28r%5E2%29%28h%29+=+%28pi%29%284%5E2%29%2812%29+=+192%28pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The portion of the cone that is inside the cylinder is similar to the whole cone.  The radii of those two cones are in the ratio 2:3; since the cones are similar, the ratio of their heights is also 2:3.  That makes the height of the small cone 2/3 of 9, which is 6.  Then the volume of the cone that is inside the cylinder is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%28pi%29%28r%5E2%29%28h%29+=+%281%2F3%29%28pi%29%284%5E2%29%286%29+=+32%28pi%29 ALIGN=MIDDLE  ALT=\"%281%2F3%29%28pi%29%28r%5E2%29%28h%29+=+%281%2F3%29%28pi%29%284%5E2%29%286%29+=+32%28pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER 1: The volume of water that spills from the cylinder when the cone is lowered into it is the volume of the small cone: 32pi (cm^3).<br><BR>\n" );
document.write( "The volume of water that spilled from the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28cross%28cone%29%29 ALIGN=MIDDLE  ALT=\"highlight%28cross%28cone%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > cylinder, 32pi, is 1/6 of the volume of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28cross%28cone%29%29 ALIGN=MIDDLE  ALT=\"highlight%28cross%28cone%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > cylinder.  So when the cone is removed, the volume of water in the cylinder will be 5/6 of the original volume.  Then since the cylinder has constant radius, the height of the water in the cylinder after the cone is removed is 5/6 of the full height of the cylinder.<br><BR>\n" );
document.write( "ANSWER 2: The height of water in the cylinder after the cone is removed is (5/6)*12 = 10cm.<br><BR>\n" );
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document.write( "Thanks to tutor @Ikleyn for noticing the errors in my original response, now fixed<br> </SPAN>\n" );
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