document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1100756>Question 1100756</A>: <I><SPAN STYLE=\"word-break: break-all;\"> From a solid wooden cone of height 20cm and slant height 25cm, largest possible hemisphere is carved. <BR>\n" );
document.write( "a) Find the radius of the hemisphere<BR>\n" );
document.write( "b) Find the volume of the remaining portion </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #715318 by </B><A HREF=/tutors/aboutme.mpl?userid=Fombitz><B>Fombitz(32388)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Fombitz><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=Fombitz><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=715318\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\">  <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/display-illustration.mpl?tutor=Fombitz&illustration_name=des8.JPG\">.<BR>\n" );
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document.write( "So from the diagram,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha%2Bbeta%2B90=180 ALIGN=MIDDLE  ALT=\"alpha%2Bbeta%2B90=180\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha%2Bbeta=90 ALIGN=MIDDLE  ALT=\"alpha%2Bbeta=90\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( ".<BR>\n" );
document.write( ".<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=cos%28alpha%29=r%2FCX=r%2F%2820-r%29 ALIGN=MIDDLE  ALT=\"cos%28alpha%29=r%2FCX=r%2F%2820-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%28alpha%29=20%2F25=4%2F5 ALIGN=MIDDLE  ALT=\"sin%28alpha%29=20%2F25=4%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "You also know that,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sin%5E2%28alpha%29%2Bcos%5E2%28alpha%29=1 ALIGN=MIDDLE  ALT=\"sin%5E2%28alpha%29%2Bcos%5E2%28alpha%29=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=16%2F25%2Br%5E2%2F%2820-r%29%5E2=1 ALIGN=MIDDLE  ALT=\"16%2F25%2Br%5E2%2F%2820-r%29%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%5E2%2F%2820-r%29%5E2=9%2F25 ALIGN=MIDDLE  ALT=\"r%5E2%2F%2820-r%29%5E2=9%2F25\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r%2F%2820-r%29=3%2F5 ALIGN=MIDDLE  ALT=\"r%2F%2820-r%29=3%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5r=3%2820-r%29 ALIGN=MIDDLE  ALT=\"5r=3%2820-r%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=5r=60-3r ALIGN=MIDDLE  ALT=\"5r=60-3r\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8r=60 ALIGN=MIDDLE  ALT=\"8r=60\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Solve for r.<BR>\n" );
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document.write( ".<BR>\n" );
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document.write( "The volume of the cone is,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5Bc%5D=pi%2AR%5E2%2Ah ALIGN=MIDDLE  ALT=\"V%5Bc%5D=pi%2AR%5E2%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Calculate R using the Pythagroean theorem,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=20%5E2%2BR%5E2=25%5E2 ALIGN=MIDDLE  ALT=\"20%5E2%2BR%5E2=25%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R=sqrt%28625-400%29 ALIGN=MIDDLE  ALT=\"R=sqrt%28625-400%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "and the volume of the sphere is,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5Bs%5D=%284%2F3%29pi%2Ar%5E3 ALIGN=MIDDLE  ALT=\"V%5Bs%5D=%284%2F3%29pi%2Ar%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > with r calculated above.<BR>\n" );
document.write( "So the left over volume would be,<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=V%5Bc%5D-V%5Bs%5D ALIGN=MIDDLE  ALT=\"V=V%5Bc%5D-V%5Bs%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );