document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=972689>Question 972689</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A spherical balloon is inflated, and its diameter as a function of time is given by d(t) = t + 2 . Which of the following represents the surface area of the balloon? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #595155 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=595155\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula for surface area of a sphere is S = 4*pi * R^2<BR>\n" );
document.write( "S = Surface Area of the Sphere.<BR>\n" );
document.write( "pi = 3.14159........<BR>\n" );
document.write( "R = radius of the sphere.\r<BR>\n" );
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document.write( "since radius of the sphere = 1/2 times the diameter, then this formula becomes:<BR>\n" );
document.write( "S = 4 * pi * (D/2)^2 which becomes:<BR>\n" );
document.write( "S = 4 * pi * D^2 / 4 which becomes:<BR>\n" );
document.write( "S = pi * D^2.\r<BR>\n" );
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document.write( "Since you are given that D is equal to T + 2, then it stands to reason that S will be equal to pi * (T + 2)^2.\r<BR>\n" );
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document.write( "So your formula for S would be S = pi * (T + 2)^2.\r<BR>\n" );
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document.write( "let's see if this makes sense.\r<BR>\n" );
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document.write( "you have D = T + 2.\r<BR>\n" );
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document.write( "For some sample random values of T, we get:\r<BR>\n" );
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document.write( "When T = 1, D = 3<BR>\n" );
document.write( "When T = 5, D = 7<BR>\n" );
document.write( "When T = 10, D = 12\r<BR>\n" );
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document.write( "When D = 3, S = pi * 3^2 = pi * 9<BR>\n" );
document.write( "When D = 7, S = pi * 7^2 = pi * 49<BR>\n" );
document.write( "When D = 12, S = pi * 12^2 pi * 144\r<BR>\n" );
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document.write( "using the formula of S = pi * (T + 2)^2, we get:\r<BR>\n" );
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document.write( "When T = 1, S = pi * 3^2 = pi * 9<BR>\n" );
document.write( "When T = 5, S = pi * 7^2 = pi * 49<BR>\n" );
document.write( "When T = 10, S = pi * 12^2 = pi * 144\r<BR>\n" );
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document.write( "Let's just take one of them and see if this tracks with the formula that we started with, which was S = 4*pi*R^2\r<BR>\n" );
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document.write( "When D = 7, R = 3.5 and S = 4 * pi * (3.5)^2 = 4 * pi * 12.25 = pi * 49.<BR>\n" );
document.write( "D = 7 occurs when T = 5 because D = (T + 2) becomes D = 7<BR>\n" );
document.write( "The formula for S in terms of T is S = pi * (T + 2)^2 which becomes S = pi * 7^2 which becomes S = pi * 49.\r<BR>\n" );
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document.write( "I'd go with  S = pi * (T + 2)^2.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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