document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1044876>Question 1044876</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Asking this question again as was responded too but no answer was given:\r<BR>\n" );
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document.write( "Need to find the surface area of composite figures and leave answer in terms of pi. The first figure is a cone with a radius of 10mm and a height of 24mm (does not give the slant height) and inside is a hemisphere with a radius of 8mm.  <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 #660313 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=660313\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In a right circular cone, the base 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;\" > is perpendicular to the height, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Radius, height, and slant height form a right triangle,<BR>\n" );
document.write( "and the slant height can be calculated using the Pythagorean theorem as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28h%5E2%2Br%5E2%29 ALIGN=MIDDLE  ALT=\"sqrt%28h%5E2%2Br%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So, when given <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r ALIGN=MIDDLE  ALT=\"r\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > , the lateral surface area of a right circular cone can be calculated as<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Ar%2Asqrt%28h%5E2%2Br%5E2%29 ALIGN=MIDDLE  ALT=\"pi%2Ar%2Asqrt%28h%5E2%2Br%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "With <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=24 ALIGN=MIDDLE  ALT=\"h=24\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=10 ALIGN=MIDDLE  ALT=\"r=10\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "the slant height is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%2824%5E2%2B10%5E2%29=26 ALIGN=MIDDLE  ALT=\"sqrt%2824%5E2%2B10%5E2%29=26\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and the lateral surface area is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A10%2A26=260pi ALIGN=MIDDLE  ALT=\"pi%2A10%2A26=260pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
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document.write( "I assume that your composite figure is a cone with a hemisphere taken out of the base, so that the cross section looks like this:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28240%2C280%2C-12%2C12%2C-25%2C3%2C%0D%0Agreen%28arrow%280%2C0%2C-8%2C0%29%29%2Cgreen%28arrow%28-8%2C0%2C0%2C0%29%29%2C%0D%0Agreen%28triangle%2810%2C0%2C0%2C0%2C0%2C-24%29%29%2C%0D%0Agreen%28rectangle%280%2C0%2C1%2C-1%29%29%2C%0D%0Alocate%28-4.5%2C0%2Cgreen%288%29%29%2Clocate%284.5%2C2.5%2Cgreen%2810%29%29%2C%0D%0Alocate%280.3%2C-12%2Cgreen%28h=24%29%29%2C%0D%0Agreen%28arrow%280%2C1%2C10%2C1%29%29%2Cgreen%28arrow%2810%2C1%2C0%2C1%29%29%2C%0D%0Aline%28-10%2C0%2C-8%2C0%29%2Cline%288%2C0%2C10%2C0%29%2C%0D%0Aline%28-10%2C0%2C0%2C-24%29%2Cline%2810%2C0%2C0%2C-24%29%2C%0D%0Aarc%280%2C0%2C16%2C16%2C0%2C180%29%2Clocate%285.5%2C-11%2C26%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > , and only a ring is left of the base of the cone,like this: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28240%2C240%2C-12%2C12%2C-12%2C12%2Ccircle%280%2C0%2C10%29%2C%0D%0Acircle%280%2C0%2C8%29%2Clocate%28-3.5%2C4%2Ccircular%29%2Clocate%28-2%2C2%2Chole%29%2C%0D%0Agreen%28arrow%280%2C0%2C8%2C0%29%29%2Cgreen%28arrow%288%2C0%2C0%2C0%29%29%2C%0D%0Alocate%283.5%2C0%2Cgreen%288%29%29%2Clocate%28-5.5%2C0%2Cgreen%2810%29%29%2C%0D%0Agreen%28arrow%28-2%2C0%2C-10%2C0%29%29%2Cgreen%28arrow%28-8%2C0%2C0%2C0%29%29%2C%0D%0Alocate%28-1.5%2C-8%2Cring%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
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document.write( "The surface area of that ring that is left over of the base of the cone<BR>\n" );
document.write( "is the area of a circle of radius <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "minus the area of a circle of radius <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > ;<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2A10%5E2-pi%2A8%5E2=100pi-64pi=36pi ALIGN=MIDDLE  ALT=\"pi%2A10%5E2-pi%2A8%5E2=100pi-64pi=36pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
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document.write( "The surface area of a sphere of radius <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=8 ALIGN=MIDDLE  ALT=\"r=8\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Api%2A8%5E2 ALIGN=MIDDLE  ALT=\"4%2Api%2A8%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "so the surface of a hemisphere of radius <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" > is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Api%2A8%5E2=2%2Api%2A64=128pi ALIGN=MIDDLE  ALT=\"2%2Api%2A8%5E2=2%2Api%2A64=128pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
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document.write( "The surface area of your composite figure is mad of three parts:<BR>\n" );
document.write( "lateral surface area of the cone =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=260pi ALIGN=MIDDLE  ALT=\"260pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "area of ring on the cone base =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=36pi ALIGN=MIDDLE  ALT=\"36pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and<BR>\n" );
document.write( "area of hemisphere =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=128pi ALIGN=MIDDLE  ALT=\"128pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Total surface area =<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=260pi%2B36pi%2B128pi=highlight%28424pi%29 ALIGN=MIDDLE  ALT=\"260pi%2B36pi%2B128pi=highlight%28424pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > .  </SPAN>\n" );
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