document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187680>Question 1187680</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The surface area of a sphere varies directly as the square of the radius. If the surface <BR>\n" );
document.write( "area is 36𝜋 𝑖𝑛<BR>\n" );
document.write( "2 when the radius is 3 inches, what is the surface area of the sphere with <BR>\n" );
document.write( "a radius of 5 inches? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #818702 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=818702\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the direct variation formula is y = k * x\r<BR>\n" );
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document.write( "when x = r^2, the formula becomes y = k * r^2.\r<BR>\n" );
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document.write( "when r = 3 and y = 36 * pi, the formula becomes 36 * pi = k * 3^2\r<BR>\n" );
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document.write( "simplify to get 36 * pi = k * 9\r<BR>\n" );
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document.write( "solve for k to get k = 36 * pi / 9 = 4 * pi.\r<BR>\n" );
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document.write( "now that you have the value of k, you can solve for y when r = 5.\r<BR>\n" );
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document.write( "the formula of y = k * r^2 becomes y = 4 * pi * 5^2 which becomes y = 4 * pi * 25 which becomes y = 100 * pi.\r<BR>\n" );
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document.write( "k, being the constant of variation, doesn't change, as long as you're dealint with the surface area of a sphere.\r<BR>\n" );
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document.write( "if you look up the formula for the surface area of a sphere, you will find that the formula is y = 4 * pi * r^2, where y is the surface area of the sphere.<BR>\n" );
document.write( "4 * pi remains the same, regardless of the measure of the radius.<BR>\n" );
document.write( "it becomes the constant of variation in that formula.\r<BR>\n" );
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