document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203307>Question 1203307</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The ratio of the altitude of a zone to the diameter of the sphere on which it is 1:5. The area of the zone is 80 pi. Find the area of the sphere. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838777 by </B><A HREF=/tutors/aboutme.mpl?userid=ikleyn><B>ikleyn(52781)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ikleyn><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=ikleyn><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=838777\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> .\r<BR>\n" );
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document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The solution by @MathLover1 is incorrect.<BR>\n" );
document.write( "&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;I came to bring you a correct solution.\r<BR>\n" );
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document.write( "Surface area of a sphere: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=4%2Api%2Ar%5E2 ALIGN=MIDDLE  ALT=\"A=4%2Api%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "let altitude be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" > and diameter <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=d ALIGN=MIDDLE  ALT=\"d\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "given ratio is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%3A5 ALIGN=MIDDLE  ALT=\"1%3A5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h%2Fd=1%2F5 ALIGN=MIDDLE  ALT=\"h%2Fd=1%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=d%2F5 ALIGN=MIDDLE  ALT=\"h=d%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=d%2F2+ ALIGN=MIDDLE  ALT=\"r=d%2F2+\"   DISABLED_style= \"max-width:90%; height:auto;\" > &nbsp;&nbsp;--> &nbsp;&nbsp;<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h=%282r%29%2F5 ALIGN=MIDDLE  ALT=\"h=%282r%29%2F5\"   DISABLED_style= \"max-width:90%; height:auto;\" >  &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<<<---===  &nbsp;&nbsp;it is where &nbsp;@MathLover1 &nbsp;made her mistake.\r<BR>\n" );
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document.write( "The area <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A ALIGN=MIDDLE  ALT=\"A\"   DISABLED_style= \"max-width:90%; height:auto;\" > of a spherical zone can be calculated using the formula \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=2%2Api%2Arh+ ALIGN=MIDDLE  ALT=\"A=2%2Api%2Arh+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "where <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h+ ALIGN=MIDDLE  ALT=\"h+\"   DISABLED_style= \"max-width:90%; height:auto;\" >is the height of the spherical zone 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;\" > is the radius of the sphere.\r<BR>\n" );
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document.write( "if  the area of the  spherical zone  is  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80pi ALIGN=MIDDLE  ALT=\"80pi\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  we have\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=80pi=2%2Api%2Arh ALIGN=MIDDLE  ALT=\"80pi=2%2Api%2Arh\"   DISABLED_style= \"max-width:90%; height:auto;\" >...simplify\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40=rh ALIGN=MIDDLE  ALT=\"40=rh\"   DISABLED_style= \"max-width:90%; height:auto;\" >.....substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=h ALIGN=MIDDLE  ALT=\"h\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=40=r%2A%282r%29%2F5%29 ALIGN=MIDDLE  ALT=\"40=r%2A%282r%29%2F5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=100=r%5E2 ALIGN=MIDDLE  ALT=\"100=r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=sqrt%28100%29 ALIGN=MIDDLE  ALT=\"r=sqrt%28100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<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;\" >\r<BR>\n" );
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document.write( "then, surface area of a sphere is: \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=4%2Api%2A10%5E2 ALIGN=MIDDLE  ALT=\"A=4%2Api%2A10%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=4%2Api%2A100 ALIGN=MIDDLE  ALT=\"A=4%2Api%2A100\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=400%2Api ALIGN=MIDDLE  ALT=\"A=400%2Api\"   DISABLED_style= \"max-width:90%; height:auto;\" >    &nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<U>ANSWER</U>\r<BR>\n" );
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document.write( "Solved &nbsp;&nbsp;(correctly).\r<BR>\n" );
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document.write( " </SPAN>\n" );
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