document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=98505>Question 98505</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A circular sheet of paper of radius 6 cm is cut into three equal sectors, and each sector is formed into a cone with no overlap. What is the height in centimeters of each cone? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #71676 by </B><A HREF=/tutors/aboutme.mpl?userid=Earlsdon><B>Earlsdon(6294)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Earlsdon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=71676\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> We could find the height of the resulting cone if we knew their slant-height and radius.<BR>\n" );
document.write( "Starting with the circular sheet of paper whose radius (R) is 6 cm. If you divide this into three equal sectors to form the cones, then each cone will have a slant-height equal to the radius of the original circle, right?<BR>\n" );
document.write( "Now the circumference of the base of each cone will be equal to one third of the circumference of the original circle.<BR>\n" );
document.write( "The circumference (C) of the original circle is:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+2%28pi%29R ALIGN=MIDDLE  ALT=\"C+=+2%28pi%29R\"   DISABLED_style= \"max-width:90%; height:auto;\" > and, of course, you know that R is 6 cm, so...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C+=+12%28pi%29 ALIGN=MIDDLE  ALT=\"C+=+12%28pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Divide both sides by 3 to find one third of this.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=C%2F3+=+4%28pi%29 ALIGN=MIDDLE  ALT=\"C%2F3+=+4%28pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and this is the circumference (c) of the cone base.<BR>\n" );
document.write( "From this we can find the radius (r) of the cone base because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c+=+2%28pi%29r ALIGN=MIDDLE  ALT=\"c+=+2%28pi%29r\"   DISABLED_style= \"max-width:90%; height:auto;\" > but this is equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28pi%29 ALIGN=MIDDLE  ALT=\"4%28pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. So we can write:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28pi%29r+=+4%28pi%29 ALIGN=MIDDLE  ALT=\"2%28pi%29r+=+4%28pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Simplifying, we get:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2r+=+4 ALIGN=MIDDLE  ALT=\"2r+=+4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and so...<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+2 ALIGN=MIDDLE  ALT=\"r+=+2\"   DISABLED_style= \"max-width:90%; height:auto;\" > this is the radius of the cone base.<BR>\n" );
document.write( "Now we can use the Pythagorean theorem to find the cone height using the slant-height of the cone (6 cm) as the hypotenuse of a right triangle and the radius of the cone base (2 cm) as the base of a right triangle.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%5E2+=+2%5E2+%2B+h%5E2 ALIGN=MIDDLE  ALT=\"6%5E2+=+2%5E2+%2B+h%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > where h is the height of the cone.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36+=+4+%2B+h%5E2 ALIGN=MIDDLE  ALT=\"36+=+4+%2B+h%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Subtract 4 from both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%5E2+=+32 ALIGN=MIDDLE  ALT=\"h%5E2+=+32\"   DISABLED_style= \"max-width:90%; height:auto;\" > Take the square root of both sides.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+=+5.657 ALIGN=MIDDLE  ALT=\"h+=+5.657\"   DISABLED_style= \"max-width:90%; height:auto;\" >cm. This is the height of the cone to the nearest thousandth. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );