document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181729>Question 1181729</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The diameter of a sphere coincides with the axis of a right circular cone, and the surface of the cone intersects the surface of the sphere in in a great circle. Find: (a) the vertical angle of the cone: (b) the volume of the cone; (c) the volume common to the two solids: (d) the volume of that portion of the cone which lies outside the sphere: (e) the volume of that portion of the sphere which lies outside the cone. Denote radius of sphere by R.\r<BR>\n" );
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document.write( "Solve Problem if (a) R=2: (b) R=3.72.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #850002 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52787)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=850002\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .<BR>\n" );
document.write( "The diameter of a sphere coincides with the axis of a right circular cone, and the surface <BR>\n" );
document.write( "of the cone intersects the surface of the sphere in in a great circle. Find: <BR>\n" );
document.write( "(a) the vertical angle of the cone: <BR>\n" );
document.write( "(b) the volume of the cone; <BR>\n" );
document.write( "(c) the volume common to the two solids: <BR>\n" );
document.write( "(d) the volume of that portion of the cone which lies outside the sphere: <BR>\n" );
document.write( "(e) the volume of that portion of the sphere which lies outside the cone. Denote radius of sphere by R.\r<BR>\n" );
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document.write( "Solve Problem if (a) R=2: (b) R=3.72.<BR>\n" );
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document.write( "The solution in the post by @CPhill is INCORRECT.\r<BR>\n" );
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document.write( "It is incorrect, since @CPhill incorrectly interprets the problem.\r<BR>\n" );
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document.write( "He solves the problem in assumption that the cone TOUCHES the sphere <BR>\n" );
document.write( "along a great circle.\r<BR>\n" );
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document.write( "But, firstly, it is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28highlight%28IMPOSSIBLE%29%29 ALIGN=MIDDLE  ALT=\"highlight%28highlight%28IMPOSSIBLE%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and, secondly, the problem <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28highlight%28tells%29%29 ALIGN=MIDDLE  ALT=\"highlight%28highlight%28tells%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > something <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28highlight%28DIFFERENT%29%29 ALIGN=MIDDLE  ALT=\"highlight%28highlight%28DIFFERENT%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "It says that the cone' surface <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28highlight%28INTERSECTS%29%29 ALIGN=MIDDLE  ALT=\"highlight%28highlight%28INTERSECTS%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > the sphere surface at the great circle,<BR>\n" );
document.write( "which is totally different condition.\r<BR>\n" );
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document.write( "Thus, the value of @CPhill' solution is ZERO.\r<BR>\n" );
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document.write( "He is just deceiving you.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Regarding the post by @CPhill . . . \r<BR>\n" );
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document.write( "Keep in mind that @KPhill is a pseudonym for the Google artificial intelligence.\r<BR>\n" );
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document.write( "The artificial intelligence is like a baby now. It is in the experimental stage <BR>\n" );
document.write( "of development and can make mistakes and produce nonsense without any embarrassment.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;It has no feeling of shame - it is shameless.\r<BR>\n" );
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document.write( "This time, again, &nbsp;it made an error.\r<BR>\n" );
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document.write( "Although the @CPhill' solution are copy-paste &nbsp;Google &nbsp;AI solutions, &nbsp;there is one essential difference.\r<BR>\n" );
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document.write( "Every time, &nbsp;Google &nbsp;AI &nbsp;makes a note at the end of its solutions that &nbsp;Google &nbsp;AI &nbsp;is experimental<BR>\n" );
document.write( "and can make errors/mistakes.\r<BR>\n" );
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document.write( "All @CPhill' solutions are copy-paste of &nbsp;Google &nbsp;AI &nbsp;solutions, with one difference:<BR>\n" );
document.write( "@PChill never makes this notice and never says that his solutions are copy-past that of Google.\r<BR>\n" );
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document.write( "So, &nbsp;in my view, &nbsp;doing this way, &nbsp;this guy, &nbsp;@CPhill, &nbsp;simply makes dishonest business at this forum.\r<BR>\n" );
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document.write( "Every time, &nbsp;@CPhill embarrasses to tell the truth.\r<BR>\n" );
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document.write( "But I am not embarrassing to tell the truth, &nbsp;as it is my duty at this forum.\r<BR>\n" );
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document.write( "And the last my comment.\r<BR>\n" );
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document.write( "When you obtain such posts from @CPhill, &nbsp;remember, &nbsp;that &nbsp;NOBODY &nbsp;is responsible for their correctness, <BR>\n" );
document.write( "until the specialists and experts will check and confirm their correctness.\r<BR>\n" );
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document.write( "Without it, &nbsp;their reliability is &nbsp;ZERO and their creadability is &nbsp;ZERO, &nbsp;too.\r<BR>\n" );
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document.write( "Special note for a visitor who posted this problem.\r<BR>\n" );
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document.write( "It borders on madness to pack 5 (five) questions into one post.\r<BR>\n" );
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document.write( "The rules of this forum allow one question per post.\r<BR>\n" );
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document.write( "Even if assume that the rules are made of rubber, then 3 questions per post is the maximum.\r<BR>\n" );
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document.write( "Every time, as you violate this rule, you EITHER will wait several years, OR will get a mess.\r<BR>\n" );
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document.write( "Regarding the rules of this forum, see this page\r<BR>\n" );
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document.write( "https://www.algebra.com/tutors/students/ask.mpl?action=ask_question&topic=Equations&return_url=http://www.algebra.com/algebra/homework/equations/\r<BR>\n" );
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document.write( "from which you post your problems.\r<BR>\n" );
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document.write( "It is assumed that you read these rules before posting.\r<BR>\n" );
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document.write( "It is also assumed that you do understand what is written in that page and follow the rules.\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Those who violate them, &nbsp;work against their own interests.\r<BR>\n" );
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