document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1789>Question 1789</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A rectangular piece of sheet metal with an area of 1200 in^2 is to be bent into a cylindrical length (right circular cylinder) of stovepipe having a volume of 600 in^3. What are the dimensions of the sheet metal? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #625 by </B><A HREF=/tutors/aboutme.mpl?userid=longjonsilver><B>longjonsilver(2297)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=longjonsilver><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=longjonsilver><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=625\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> these sorts of questions are lovely questions (yes, i guess i must be a sad individual)...anyway, draw a rectangle, vertical side a and horizontal side b\r<BR>\n" );
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document.write( "the area = ab = 1200\r<BR>\n" );
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document.write( "Now draw an upright cylinder (by wrapping the length b into a circle)...its radius is length r, and its height is a\r<BR>\n" );
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document.write( "Volume of this cyclinder is the area of the circular end times the height...\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=volume+=+pi%2Ar%5E2%2Aa ALIGN=MIDDLE  ALT=\"volume+=+pi%2Ar%5E2%2Aa\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "now, seeing as how i do not know what r is, i had better find it. This is found from the circumference of the circle (which is the length b)...\r<BR>\n" );
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document.write( "circumference, b = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2Api%2Ar ALIGN=MIDDLE  ALT=\"2%2Api%2Ar\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r+=+b%2F%282%2Api%29 ALIGN=MIDDLE  ALT=\"r+=+b%2F%282%2Api%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So, we can get rid of the r in the volume equation..this is now re-written as:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=volume+=+pi%2A+%28b%2F2%2Api%29%5E2+%2A+a ALIGN=MIDDLE  ALT=\"volume+=+pi%2A+%28b%2F2%2Api%29%5E2+%2A+a\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=volume+=+%28pi%2Aa%2Ab%5E2%29%2F%284%2A%28pi%29%5E2%29 ALIGN=MIDDLE  ALT=\"volume+=+%28pi%2Aa%2Ab%5E2%29%2F%284%2A%28pi%29%5E2%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >. This can be simplified to\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=volume+=+%28a%2Ab%5E2%29%2F%284%2Api%29 ALIGN=MIDDLE  ALT=\"volume+=+%28a%2Ab%5E2%29%2F%284%2Api%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So we know the volume, but not a or b...2 unknowns in 1 equation is NOT good, so we need to get rid of either a or b...we do this by using the area equation, at the start of this explanation...let's re-write it as a = 1200/b\r<BR>\n" );
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document.write( "so we now get <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=volume+=+%281200b%5E2%29%2F%284%2Ab%2Api%29 ALIGN=MIDDLE  ALT=\"volume+=+%281200b%5E2%29%2F%284%2Ab%2Api%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "cancel the b with one of those in the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b%5E2 ALIGN=MIDDLE  ALT=\"b%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > term, and simplifying the 1200 and 4 gives\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=volume+=+%28300b%29%2F%28pi%29 ALIGN=MIDDLE  ALT=\"volume+=+%28300b%29%2F%28pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=600+=+300b%2Fpi ALIGN=MIDDLE  ALT=\"600+=+300b%2Fpi\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b+=+%28600pi%29%2F%28300%29 ALIGN=MIDDLE  ALT=\"b+=+%28600pi%29%2F%28300%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > --> b=2pi\r<BR>\n" );
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document.write( "Substitute this into the area equation and you find a=600/pi. These are the dimensions of the sheet metal.\r<BR>\n" );
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document.write( "cheers<BR>\n" );
document.write( "Jon. </SPAN>\n" );
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