document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1082549>Question 1082549</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The surface area of a cylinder is 600 pi centimeters squared. If the radius is 1 cm, find the volume in terms of pi. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #696613 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=696613\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the formula for surface area of a cylinder is:\r<BR>\n" );
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document.write( "s = 2*pi*r^2 + 2*pi*r*h\r<BR>\n" );
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document.write( "since you know the surface area is equal to 600 square meters and the radius is equal to 1, this formula becomes:\r<BR>\n" );
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document.write( "600 = 2*pi*1^2 + 2*pi*1*h\r<BR>\n" );
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document.write( "since 1^2 = 1 and anything times 1 is anything, this formula becomes:\r<BR>\n" );
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document.write( "600 = 2*pi + 2*pi*h\r<BR>\n" );
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document.write( "factor out the 2*pi and the formula becomes:\r<BR>\n" );
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document.write( "600 = 2*pi*(1+h)\r<BR>\n" );
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document.write( "divide both sides of this equation by 2*pi and you get:\r<BR>\n" );
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document.write( "600/(2*pi) = 1+h\r<BR>\n" );
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document.write( "the parentheses are necessary since you are dividing by (2*pi).<BR>\n" );
document.write( "without them, you would have 600/2*pi which would divide 600 by 2 and then multiply the result by pi - a totally different result.\r<BR>\n" );
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document.write( "subtract 1 from both sides of this equation to get:\r<BR>\n" );
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document.write( "600/(2*pi)-1 = h\r<BR>\n" );
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document.write( "solve for h to get h = 94.49296586\r<BR>\n" );
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document.write( "the formula for the volume of a cylinder is v = pi*r^2*h\r<BR>\n" );
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document.write( "since r = 1, then r^2 = 1 and the formula becomes v = pi*h\r<BR>\n" );
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document.write( "since h = 94.49296586, then the formula becomes v = 94.49296586*pi\r<BR>\n" );
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document.write( "solve for v to get v = 296.8584073 cubic meters.\r<BR>\n" );
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document.write( "while this is correct, it might not be what you were asked to do.\r<BR>\n" );
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document.write( "i believe you were asked to find the volume in terms of pi.\r<BR>\n" );
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document.write( "in that case, you would do the following:\r<BR>\n" );
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document.write( "s = 2*pi*r^2 + 2*pi*r*h\r<BR>\n" );
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document.write( "since r = 1, this becomes:\r<BR>\n" );
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document.write( "s = 2*pi + 2*pi*h\r<BR>\n" );
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document.write( "factor out the 2*pi and you get s = 2*pi*(1+h)\r<BR>\n" );
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document.write( "since s = 600 square meters, you get 600 = 2*pi*(1+h)\r<BR>\n" );
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document.write( "solve for h to get h = 600/(2*pi)-1.\r<BR>\n" );
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document.write( "volume formula is v = pi*r^2*h\r<BR>\n" );
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document.write( "since h = 600/(2*pi)-1, the formula becomes v = pi*r^2*(600/(2*pi)-1).\r<BR>\n" );
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document.write( "simplify to get v = pi*r^2*600/(2*pi) - pi*r^2*1\r<BR>\n" );
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document.write( "simplify further to get v = r^2*600/2 - pi*r^2\r<BR>\n" );
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document.write( "simplify further to get v = 300*r^2 - pi*r^2\r<BR>\n" );
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document.write( "since r = 1, this simplifies further to v = 300 - pi\r<BR>\n" );
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document.write( "that's your volume in terms of pi.\r<BR>\n" );
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document.write( "evaluate this to get v = = 296.8584073 cubic meters.\r<BR>\n" );
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document.write( "that's what we got before when we have determined the value of h.\r<BR>\n" );
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document.write( "this time, however, the volume is in terms of pi as requested by the problem statement.\r<BR>\n" );
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document.write( "your solution is that v = 300 - pi.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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