document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1143219>Question 1143219</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A paper cup is in the shape of a right circular cone with a diameter of 8cm and a height of 12cm.\r<BR>\n" );
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document.write( "a.) Suppose the cup is filled with water to a depth of 8cm. Calculate the volume of water in the cup. Round to the nearest whole number. (HINT: Use similar triangles.)\r<BR>\n" );
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document.write( "b.) To what depth must the cup be filled in order to be half full of water? Round to the nearest tenth. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #764018 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=764018\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <br><BR>\n" );
document.write( "The volume of the cup is<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+%281%2F3%29%28pi%29%28r%5E2%29%28h%29+=+%281%2F3%29%28pi%29%284%5E2%29%2812%29+=+64%28pi%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "a. If the cup is filled to a depth of 8cm, that is 2/3 the full depth, so the radius of the water in the cup will be 2/3 of the full radius, which is 8/3cm.  The volume of water is then<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+%281%2F3%29%28pi%29%28%288%2F3%29%5E2%29%288%29+=+%28512%2F27%29pi ALIGN=MIDDLE  ALT=\"V+=+%281%2F3%29%28pi%29%28%288%2F3%29%5E2%29%288%29+=+%28512%2F27%29pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "Since the question asks for an answer as the nearest whole number, perform the calculation and round as required.<br><BR>\n" );
document.write( "Note that, though the problem gives a hint about using similar triangles, there is a much faster way to answer this question.  If the height of the water in the cup is 2/3 the full height of the cup, then the volume of water in the cup is (2/3)^3 of the total volume:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%282%2F3%29%5E3%29%2864pi%29+=+%28512%2F27%29pi ALIGN=MIDDLE  ALT=\"%28%282%2F3%29%5E3%29%2864pi%29+=+%28512%2F27%29pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "b. This question is answered far more easily using the concept noted above.<br><BR>\n" );
document.write( "If the volume is 1/2 of the total volume, then the height of the cone (depth of the water) is the full height, multiplied by the CUBE ROOT of 1/2.<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+12%2A%281%2F2%29%5E%281%2F3%29+=+9.5244 ALIGN=MIDDLE  ALT=\"h+=+12%2A%281%2F2%29%5E%281%2F3%29+=+9.5244\"   DISABLED_style= \"max-width:90%; height:auto;\" > to 4 decimal places.<br><BR>\n" );
document.write( "Than round as directed. </SPAN>\n" );
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