document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1037863>Question 1037863</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A sector of a circle 7cm subtending an angle 210 at the centre of the circle, is used to form a cone. calculate to the nearest whole number, the base radius of a cone?, height of the cone?, total surface area of a cone?, volume of the cone and vertical angle of the cone </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #652566 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=652566\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Is the 7cm measure the radius of the circle? Or is it the diameter?<BR>\n" );
document.write( " <BR>\n" );
document.write( "Assuming the radius is 7cm,<BR>\n" );
document.write( "that would be the slant height of the cone<BR>\n" );
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document.write( "The circumference of the circle measures <BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Api%2A%287cm%29=14pi ALIGN=MIDDLE  ALT=\"2%2Api%2A%287cm%29=14pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm ALIGN=MIDDLE  ALT=\"cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The curved edge of the sector measures <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=210%2F360=7%2F12 ALIGN=MIDDLE  ALT=\"210%2F360=7%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > as much as the total circumference, or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%2F12%2914pi ALIGN=MIDDLE  ALT=\"%287%2F12%2914pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm=49pi%2F6 ALIGN=MIDDLE  ALT=\"cm=49pi%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm ALIGN=MIDDLE  ALT=\"cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and that length becomes the circumference of the base of a cone of radius <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > , so<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2Ar=49pi%2F6 ALIGN=MIDDLE  ALT=\"2pi%2Ar=49pi%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm ALIGN=MIDDLE  ALT=\"cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2Ar=49pi%2F6 ALIGN=MIDDLE  ALT=\"2pi%2Ar=49pi%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm ALIGN=MIDDLE  ALT=\"cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > ---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=49pi%2F12pi=49%2F12 ALIGN=MIDDLE  ALT=\"r=49pi%2F12pi=49%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm=approximately4.08cm=approximately ALIGN=MIDDLE  ALT=\"cm=approximately4.08cm=approximately\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%284cm%29 ALIGN=MIDDLE  ALT=\"highlight%284cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded to the nearest whole number).<BR>\n" );
document.write( " <BR>\n" );
document.write( "A cross section of the cone looks like this triangle:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C240%2C-5%2C5%2C-1%2C7%2C%0D%0Agreen%28triangle%280%2C0%2C4%2C0%2C0%2C5.7%29%29%2C%0D%0Agreen%28rectangle%280%2C0%2C0.5%2C0.5%29%29%2C%0D%0Atriangle%28-4%2C0%2C4%2C0%2C0%2C5.69%29%2C%0D%0Alocate%28-0.25%2C3%2Cgreen%28h%29%29%2C%0D%0Alocate%28-2.2%2C0.5%2Cr%29%2C%0D%0Alocate%28-2%2C2.85%2C7cm%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The altitude of length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28h%29 ALIGN=MIDDLE  ALT=\"green%28h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > divides the triangle into two right triangles.<BR>\n" );
document.write( "In each of them the legs measure <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28h%29 ALIGN=MIDDLE  ALT=\"green%28h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and the hypotenuse mesures <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=7cm ALIGN=MIDDLE  ALT=\"7cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Using the Pythagorean theorem, and the approximate value <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=4cm ALIGN=MIDDLE  ALT=\"r=4cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "we can calculate <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28h%29 ALIGN=MIDDLE  ALT=\"green%28h%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > :<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28h%29%5E2%2B%284cm%29%5E2=%287cm%29%5E2 ALIGN=MIDDLE  ALT=\"green%28h%29%5E2%2B%284cm%29%5E2=%287cm%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28h%29%5E2%2B16cm%5E2=49cm%5E2 ALIGN=MIDDLE  ALT=\"green%28h%29%5E2%2B16cm%5E2=49cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28h%29%5E2=49cm%5E2-16cm%5E2 ALIGN=MIDDLE  ALT=\"green%28h%29%5E2=49cm%5E2-16cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28h%29%5E2=33cm%5E2 ALIGN=MIDDLE  ALT=\"green%28h%29%5E2=33cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=green%28h%29=sqrt%2833%29 ALIGN=MIDDLE  ALT=\"green%28h%29=sqrt%2833%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm=about5.74cm ALIGN=MIDDLE  ALT=\"cm=about5.74cm\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "So, The height of the cone, to the nearest whole cm is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%286cm%29 ALIGN=MIDDLE  ALT=\"highlight%286cm%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "The surface area of the a whole circle of radius 7cm is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A%287cm%29%5E2=49pi ALIGN=MIDDLE  ALT=\"pi%2A%287cm%29%5E2=49pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm%5E2 ALIGN=MIDDLE  ALT=\"cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The surface area of the sector is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=210%2F360=7%2F12 ALIGN=MIDDLE  ALT=\"210%2F360=7%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" > as much as the surface area of the a whole circle, or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%2F12%29%2A49pi ALIGN=MIDDLE  ALT=\"%287%2F12%29%2A49pi\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm%5E2=343pi%2F12 ALIGN=MIDDLE  ALT=\"cm%5E2=343pi%2F12\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm%5E2=about89.79 ALIGN=MIDDLE  ALT=\"cm%5E2=about89.79\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm%5E2 ALIGN=MIDDLE  ALT=\"cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "(If you use the approximation <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi=22%2F7 ALIGN=MIDDLE  ALT=\"pi=22%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "the area of the a whole circle is calculated as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A%287cm%29%5E2=%2822%2F7%2949 ALIGN=MIDDLE  ALT=\"pi%2A%287cm%29%5E2=%2822%2F7%2949\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm%5E2=154cm%5E2 ALIGN=MIDDLE  ALT=\"cm%5E2=154cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and the area of the sector is calculated as <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%287%2F12%29%28154cm%5E2%29=%28539%2F6%29 ALIGN=MIDDLE  ALT=\"%287%2F12%29%28154cm%5E2%29=%28539%2F6%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm%5E2 ALIGN=MIDDLE  ALT=\"cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "which is about<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=540%2F6 ALIGN=MIDDLE  ALT=\"540%2F6\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cm%5E2=90cm%5E2 ALIGN=MIDDLE  ALT=\"cm%5E2=90cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ).<BR>\n" );
document.write( "The surface of the sector becomes the lateral surface of the cone,<BR>\n" );
document.write( "so the lateral surface area of the cone is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90cm%5E2 ALIGN=MIDDLE  ALT=\"90cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (to the nearest whole number).<BR>\n" );
document.write( " <BR>\n" );
document.write( "It is not clear from the problem is what is asked for is the total surface area of a cone with those dimensions, or just the lateral area.<BR>\n" );
document.write( "The base of the cone, which was not formed out of the sector of the circle,<BR>\n" );
document.write( "is a circle of radius <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=approximately4cm ALIGN=MIDDLE  ALT=\"r=approximately4cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > as found above.<BR>\n" );
document.write( "The total surface area of a cone with those dimensions is the lateral surface plus the area of the base.<BR>\n" );
document.write( "The area of a circle of radius 4cm is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A%284cm%29%5E2=pi%2A16cm%5E2=about50cm%5E2 ALIGN=MIDDLE  ALT=\"pi%2A%284cm%29%5E2=pi%2A16cm%5E2=about50cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > (to the nearest whole number),<BR>\n" );
document.write( "so the total surface area for a cone like the one in the problem would be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90cm%5E2%2B40cm%5E2=130cm%5E2 ALIGN=MIDDLE  ALT=\"90cm%5E2%2B40cm%5E2=130cm%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "The volume of a cone with base radius <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=4cm ALIGN=MIDDLE  ALT=\"r=4cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > and height <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=6cm ALIGN=MIDDLE  ALT=\"h=6cm\"   DISABLED_style= \"max-width:90%; height:auto;\" > is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%2Api%2A%284cm%29%5E2%2A%286cm%29=approximately ALIGN=MIDDLE  ALT=\"%281%2F3%29%2Api%2A%284cm%29%5E2%2A%286cm%29=approximately\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%28101cm%5E3%29 ALIGN=MIDDLE  ALT=\"highlight%28101cm%5E3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > (to the nearest whole number).<BR>\n" );
document.write( " <BR>\n" );
document.write( "The vertical angle can be calculated from the cross section measurements><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28300%2C240%2C-5%2C5%2C-1%2C7%2C%0D%0Agreen%28triangle%280%2C0%2C4%2C0%2C0%2C5.7%29%29%2C%0D%0Agreen%28rectangle%280%2C0%2C0.5%2C0.5%29%29%2C%0D%0Atriangle%28-4%2C0%2C4%2C0%2C0%2C5.69%29%2C%0D%0Alocate%28-2.2%2C0.5%2C4cm%29%2C%0D%0Alocate%28-2%2C2.85%2C7cm%29%2C%0D%0Ared%28arc%280%2C5.7%2C3%2C3%2C90%2C124.85%29%29%2C%0D%0Alocate%28-0.7%2C4.3%2Cred%28A%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > . <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28red%28A%29%29=4cm%2F%227+cm%22=about0.60825 ALIGN=MIDDLE  ALT=\"sin%28red%28A%29%29=4cm%2F%227+cm%22=about0.60825\"   DISABLED_style= \"max-width:90%; height:auto;\" > (rounded).<BR>\n" );
document.write( "From that we get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=red%28A%29=approximately34.85%5Eo ALIGN=MIDDLE  ALT=\"red%28A%29=approximately34.85%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and the vertical angle is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2red%28A%29=about2%2A34.85%5Eo=about69.7%5Eo ALIGN=MIDDLE  ALT=\"2red%28A%29=about2%2A34.85%5Eo=about69.7%5Eo\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So the vertical angle of the cone (in whole degrees is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=highlight%2870%5Eo%29 ALIGN=MIDDLE  ALT=\"highlight%2870%5Eo%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );