document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=967660>Question 967660</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hello, the following problem involves with finding the radius of a cylinder with just the surface area given. I tried plugging in these values but the book has a different answer. Could someone please help with clarification. \r<BR>\n" );
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document.write( "Here is the problem:\r<BR>\n" );
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document.write( "S = 2&#960;rh \r<BR>\n" );
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document.write( "Given values are:\r<BR>\n" );
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document.write( "S = 120&#960;, h = 10 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #591419 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=591419\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you are given that S = 2 * pi * r * h.\r<BR>\n" );
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document.write( "that would be the lateral area only.\r<BR>\n" );
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document.write( "it does not include the area of the bases.\r<BR>\n" );
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document.write( "if the formula you show is the formula you are given, then:\r<BR>\n" );
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document.write( "S = 2 * pi * r * h becomes 120 = 2 * pi * r * 10.\r<BR>\n" );
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document.write( "simplify to get 120 = 20 * pi * r\r<BR>\n" );
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document.write( "divide both sides of the equation by (20 * pi) and you get:\r<BR>\n" );
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document.write( "120 / (20 * pi) = r\r<BR>\n" );
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document.write( "solve for r to get r = 6 / pi.\r<BR>\n" );
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document.write( "you can leave it that way or you can simplify further to get r = 1.909859317.\r<BR>\n" );
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document.write( "you can confirm by replacing r with 1.909859317 and you will get 120 = 120.\r<BR>\n" );
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document.write( "now, the surface area of of a right cylinder is equal to the lateral area plus the base area.\r<BR>\n" );
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document.write( "that formula is S = 2 * pi * r * h + 2 * pi * r^2.\r<BR>\n" );
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document.write( "that's going to make a difference in what the radius turns out to be.\r<BR>\n" );
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document.write( "if that's the formula you need, then:\r<BR>\n" );
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document.write( "S = 2 * pi * r * h + 2 * pi * r^2 becomes:\r<BR>\n" );
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document.write( "120 = 2 * pi * r * 10 + 2 * pi * r^2 \r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "120 = 20 * pi * r + 2 * pi * r^2\r<BR>\n" );
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document.write( "subtract 120 from both sides of the equation and re-arrange the terms and commute the equation to get:\r<BR>\n" );
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document.write( "2 * pi * r^2 + 20 * pi * r - 120 = 0\r<BR>\n" );
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document.write( "that's a quadratic equation in standard form that can be solved using the quadratic formula.\r<BR>\n" );
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document.write( "you will get:\r<BR>\n" );
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document.write( "Roots: -11.64067716, 1.640677162\r<BR>\n" );
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document.write( "negative value is no good.\r<BR>\n" );
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document.write( "r has to be 1.640677162 if we did everything correctly.\r<BR>\n" );
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document.write( "confirm by replacing that value of r in the original equation with 1.640677162 and you will see that the surface area is equal to 120.\r<BR>\n" );
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document.write( "here's an online calculator to give you the surface area of cylinder.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.google.com/?gws_rd=ssl#q=surface+areea+of+a+cylinder\" target = \"_blank\">https://www.google.com?gws_rd=ssl#q=surface+areea+of+a+cylinder</a>\r<BR>\n" );
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document.write( "here's what the output looks like after you enter 1.64...... for the radius and 10 for the height.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2015/050201.jpg\" alt=\"$$$\" </>\r<BR>\n" );
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document.write( "the quadratic formula is:\r<BR>\n" );
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document.write( "<PRE STYLE=\"white-space: pre-wrap; white-space: -moz-pre-wrap; white-space: -pre-wrap; white-space: -o-pre-wrap; word-wrap: break-word;\">\r\n" );
document.write( "               (-b plus or minus sqrt(b^2 - 4ac)\r\n" );
document.write( "         x =   -----------------------------------\r\n" );
document.write( "                                (2a)\r\n" );
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document.write( "your quadratic equation is :\r<BR>\n" );
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document.write( "2 * pi * r^2 + 20 * pi * r - 120 = 0\r<BR>\n" );
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document.write( "a = 2 * pi<BR>\n" );
document.write( "b = 20 * pi<BR>\n" );
document.write( "c = -120\r<BR>\n" );
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document.write( " </SPAN>\n" );
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