document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203312>Question 1203312</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The area of a zone is 50.265 sq. cm. if the altitude of the zone is 2 cm, solve the surface 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 #838756 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=838756\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "According to Wolfram MathWorld,<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://mathworld.wolfram.com/Zone.html\">https://mathworld.wolfram.com/Zone.html</a><BR>\n" );
document.write( "A zone is like a partial bit of the sphere's surface. We can think of it like a small piece of an orange peel. That link marks the zone in blue.\r<BR>\n" );
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document.write( "Here's another article talking about the topic<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://en.wikipedia.org/wiki/Spherical_segment\">https://en.wikipedia.org/wiki/Spherical_segment</a><BR>\n" );
document.write( "A spherical segment is a wedge-shaped 3D solid that forms after making those two parallel cuts of the sphere. The zone is then the outer surface area. \r<BR>\n" );
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document.write( "On either page is the formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+2%2Api%2AR%2Ah ALIGN=MIDDLE  ALT=\"S+=+2%2Api%2AR%2Ah\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "pi = 3.14 approximately (use more decimal digits of pi to get better accuracy)<BR>\n" );
document.write( "R = radius of the sphere<BR>\n" );
document.write( "h = height aka altitude<BR>\n" );
document.write( "S = surface area of the zone\r<BR>\n" );
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document.write( "In this case we are given<BR>\n" );
document.write( "S = 50.265<BR>\n" );
document.write( "h = 2\r<BR>\n" );
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document.write( "We'll use those items to find the radius R.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+2%2Api%2AR%2Ah ALIGN=MIDDLE  ALT=\"S+=+2%2Api%2AR%2Ah\"   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=50.265+=+2%2A3.14%2AR%2A2 ALIGN=MIDDLE  ALT=\"50.265+=+2%2A3.14%2AR%2A2\"   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=50.265+=+12.56R ALIGN=MIDDLE  ALT=\"50.265+=+12.56R\"   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+=+%2850.265%29%2F%2812.56%29 ALIGN=MIDDLE  ALT=\"R+=+%2850.265%29%2F%2812.56%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+=+4.00199045 ALIGN=MIDDLE  ALT=\"R+=+4.00199045\"   DISABLED_style= \"max-width:90%; height:auto;\" > approximately\r<BR>\n" );
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document.write( "Now we can determine the surface area of the sphere<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=SA+=+4%2Api%2AR%5E2 ALIGN=MIDDLE  ALT=\"SA+=+4%2Api%2AR%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=SA+=+4%2A3.14%2A4.00199045%5E2 ALIGN=MIDDLE  ALT=\"SA+=+4%2A3.14%2A4.00199045%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=SA+=+201.16005 ALIGN=MIDDLE  ALT=\"SA+=+201.16005\"   DISABLED_style= \"max-width:90%; height:auto;\" > \r<BR>\n" );
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document.write( "<font color=red>The surface area of the entire sphere is approximately 201.16005 square cm.</font>\r<BR>\n" );
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document.write( "In a real life example, this would be the entire orange peel (as opposed to the small piece of it mentioned earlier).<BR>\n" );
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