document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1107158>Question 1107158</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello Online tutors!<BR>\n" );
document.write( "Here's my question:\r<BR>\n" );
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document.write( "The surface area of a sphere is A=4pir^2(If you didn't get that it was 4 times pi times r to the second power. All one expression.<BR>\n" );
document.write( "Rest of the question:<BR>\n" );
document.write( "If the area of a circle is the same as the surface area of a sphere, find the ratio of the radius of the sphere to the radius of the circle. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #722136 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=722136\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the area of a circle is equal to pi * r^2.\r<BR>\n" );
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document.write( "the surface area of a sphere is equal to 4 * pi * r^2.\r<BR>\n" );
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document.write( "assume the radius of the circle is x.\r<BR>\n" );
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document.write( "assume the radius of the sphere is y.\r<BR>\n" );
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document.write( "the area of the circle becomes pi * x^2\r<BR>\n" );
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document.write( "the surface area of the sphere becomes 4 * pi * y^2\r<BR>\n" );
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document.write( "let A be the surface area of the sphere.\r<BR>\n" );
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document.write( "since they're the same, let A also be the area of the circle.\r<BR>\n" );
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document.write( "you get A = pi * x^2 and A = 4 * pi * x^2\r<BR>\n" );
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document.write( "since the areas are the same, you get pi * x^2 = 4 * pi * y^2\r<BR>\n" );
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document.write( "divide both sides of this equation by pi and you get x^2 = 4 * y^2\r<BR>\n" );
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document.write( "divide both sides of this equation by y^2 and you get x^2 / y^2 = 4\r<BR>\n" );
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document.write( "take the square root of both sides of this equation and you get x/y = 2\r<BR>\n" );
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document.write( "solve for x to get x = 2y.\r<BR>\n" );
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document.write( "solve for y to get y = 1/2 * x.\r<BR>\n" );
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document.write( "x is the radius of the circle.\r<BR>\n" );
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document.write( "y is the radius of the sphere.\r<BR>\n" );
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document.write( "if the radius of the circle is 2 times the radius of the sphere, then the area of the circle will be the same as the surface area of the sphere.\r<BR>\n" );
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document.write( "if the radius of the sphere is 1/2 times the radius of the circle, then the surface area of the sphere will be the same as the area of the circle.\r<BR>\n" );
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document.write( "let's see if this is correct.\r<BR>\n" );
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document.write( "assume the radius of the circle is 8 and the radius of the sphere is 4.\r<BR>\n" );
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document.write( "the ratio of the radius of the circle to the radius of the sphere is 8/4 = 2.\r<BR>\n" );
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document.write( "the ratio of the radius of the sphere to the radius of the circle is 4/8 = 1/2.\r<BR>\n" );
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document.write( "the area of the circle is equal to pi * 8^2 which is equal to 64 * pi.\r<BR>\n" );
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document.write( "the surface area of the sphere is equal to 4 * pi * 4^2  which is equal to 4 * pi * 16 which is equal to 64 * pi.\r<BR>\n" );
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document.write( "the areas are the same which confirms that the solution is correct.\r<BR>\n" );
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document.write( "the solution is that the ratio of the radius of the sphere to the radius of the circle is 1/2.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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