document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1196414>Question 1196414</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The circular sector highlighted has a radius of 6 	cm and transforms itself into the lateral surface of a cone after gluing both dotted lines together as represented below:<BR>\n" );
document.write( "https://i.imgur.com/S0yDQc2.png<BR>\n" );
document.write( "a. What is the radius of the cone's base (in cm)<BR>\n" );
document.write( "b. What is the volume of a cone using the lateral surface and base described above?<BR>\n" );
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document.write( "For simplicity I will leave off the units in my discussion.<br><BR>\n" );
document.write( "The circular sector is 5/6 of the whole circle.  The length of the curved part of the sector is 5/6 of the circumference of a circle with radius 6: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%285%2F6%29%282pi%29%286%29=10pi ALIGN=MIDDLE  ALT=\"%285%2F6%29%282pi%29%286%29=10pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "That curved part of the sector becomes the circumference of the base of the cone.  The radius of the cone is the circumference of its base, divided by 2pi: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2810pi%29%2F%282pi%29=5 ALIGN=MIDDLE  ALT=\"%2810pi%29%2F%282pi%29=5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER a. The radius of the base of the cone is 5<br><BR>\n" );
document.write( "The slant height of the cone is the radius of the sector: 6.<br><BR>\n" );
document.write( "The radius of the base of the cone is 5; the slant height is 6; the Pythagorean Theorem tells us the height of the cone is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2811%29 ALIGN=MIDDLE  ALT=\"sqrt%2811%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<br><BR>\n" );
document.write( "The volume of the cone is one-third the area of the base, times the height:<br><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=%281%2F3%29%28%28pi%29%285%5E2%29%29%28sqrt%2811%29%29 ALIGN=MIDDLE  ALT=\"V=%281%2F3%29%28%28pi%29%285%5E2%29%29%28sqrt%2811%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "ANSWER b. The volume of the cone is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%2825%2F3%29sqrt%2811%29%29pi ALIGN=MIDDLE  ALT=\"%28%2825%2F3%29sqrt%2811%29%29pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
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