document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1059712>Question 1059712</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Ref. Question 1059604:\r<BR>\n" );
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document.write( "A coil of steel wire weighs 50 lbs., diameter 0.025 in. Steel weighs .283 lbs. / cu. in. Determine length of wire.\r<BR>\n" );
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document.write( "The wire is a regular cylinder. <BR>\n" );
document.write( "Area of circle; pi * r^2. <BR>\n" );
document.write( "3.1416 * 0.0125 * 0.0125 = 0.0049 sq. in. <BR>\n" );
document.write( "0.0049 * 1 = 0.0049 cu. in. (volume of 1 ft.) <BR>\n" );
document.write( "50 / .283 = 176.678 = 177 cu. in. (vol. of wire). <BR>\n" );
document.write( "177 / 0.0049 = 36122.48 ft.\r<BR>\n" );
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document.write( "Corrected:\r<BR>\n" );
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document.write( "3.1416 * 0.0125 * 0.0125 = 0.00049 sq. in.\r<BR>\n" );
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document.write( "0.00049 * 12 = 0.00588 (vol. of 1 ft.)\r<BR>\n" );
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document.write( "50 / .283 = 176.678 = 177 cu. in. (wire vol.)\r<BR>\n" );
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document.write( "177 / 0.00588 = 30102.04 ft.\r<BR>\n" );
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document.write( "Answer given is less.  Where am I incorrect again ?<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #674747 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=674747\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A coil of steel wire weighs 50 lbs., diameter 0.025 in. Steel weighs .283 lbs. / cu. in. Determine length of wire. <BR>\n" );
document.write( "The wire is a regular cylinder. \r<BR>\n" );
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document.write( "the volume of a cylinder is equal to pi * r^2 * h.\r<BR>\n" );
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document.write( "you are given that the diameter is .025 inches.<BR>\n" );
document.write( "since the radius is 1/2 the diameter, then the radius is .0125 inches.\r<BR>\n" );
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document.write( "steel weighs .283 pounds per cubic inch.\r<BR>\n" );
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document.write( "divide 50 pounds by .283 and you get 176.6784452 cubic inches.\r<BR>\n" );
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document.write( "multiply 176.6784452 times .283 pounds per cubic inches and you will get 50 pounds.\r<BR>\n" );
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document.write( "therefore, the volume of the cylinder is equal to 176.6784452 cubic inches.\r<BR>\n" );
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document.write( "since volume of a cylinder is equal to pi * r^2 * h, and you know that the radius is equal to .0125 inches, and you know the volume is equal to 176.6784452 cubic inches, then the formula becomes:\r<BR>\n" );
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document.write( "176.6784452= pi * (.0125)^2 * h\r<BR>\n" );
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document.write( "solve for h to get h= 176.6784452 / (pi * (.0125)^2.\r<BR>\n" );
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document.write( "you will get h = 359926.3731 inches.\r<BR>\n" );
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document.write( "if you want the answer in feet, than you have to divide by 12 to get:\r<BR>\n" );
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document.write( "h = 359926.3731 inches / 12 = 2993.86443 feet.\r<BR>\n" );
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document.write( "you shouldn't round until the very end unless they  tell you what rounded number to use.\r<BR>\n" );
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document.write( "for example, you are using 3.1416 for pi.\r<BR>\n" );
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document.write( "assuming that's what they told you to do, then your answer would be:\r<BR>\n" );
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document.write( "50 pounds divided by .283 = 176.6784452.\r<BR>\n" );
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document.write( "don't round this at this time.\r<BR>\n" );
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document.write( "v = pi * r^2 * h\r<BR>\n" );
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document.write( "solve for h to get h = v / (pi * r^2)\r<BR>\n" );
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document.write( "r is in inches, not feet.\r<BR>\n" );
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document.write( "v is in cubic inches.\r<BR>\n" );
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document.write( "pi is equal to 3.1416.\r<BR>\n" );
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document.write( "formula becomes 176.6784452 / (.0125^2 * 3.1416) = 359925.5314 inches.\r<BR>\n" );
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document.write( "divide by 12 to get 29993.79428 feet.\r<BR>\n" );
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document.write( "the difference between using the unrounded version of pi rather than the rounded version of pi is not very large,but it is there.\r<BR>\n" );
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document.write( "where i think you went wrong is here.\r<BR>\n" );
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document.write( "these two statements are suspect.\r<BR>\n" );
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document.write( "3.1416 * 0.0125 * 0.0125 = 0.0049 sq. in. <BR>\n" );
document.write( "0.0049 * 1 = 0.0049 cu. in. (volume of 1 ft.) \r<BR>\n" );
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document.write( "3.1416 * .0125 * .0125 is equal to .00049 square inches., not .0049 square inches.\r<BR>\n" );
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document.write( "also, .00049 * 1 = .00049 cubic inches is not the volume of 1 foot.\r<BR>\n" );
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document.write( "it is the volume of 1 inch.\r<BR>\n" );
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document.write( "note that your error of .0049 rather than .00049 was propagated into your second statement as well.\r<BR>\n" );
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document.write( "if the height of the cylinder is 1 inch, then the volume would be pi * r^2 * h which would be 3.1416 * .0125^2 * 1 which would be equal to .000490875 cubic inches.\r<BR>\n" );
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document.write( "you rounded the intermediate answer, which you should also not do.\r<BR>\n" );
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document.write( "you should only round at the end.\r<BR>\n" );
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document.write( "so you really have total cubic inches = 176.6784452 and you really had volume of 1 inch = .000490875.\r<BR>\n" );
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document.write( "this give you total inches of 176.6784452 / .000490875 = 359925.5314 inches.\r<BR>\n" );
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document.write( "convert that to fee by dividing by 12 and you get 29993.79428 feet.\r<BR>\n" );
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