document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1151128>Question 1151128</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Which has greater volume <BR>\n" );
document.write( ". A piece of paper rolled into a cylinder Lengthwise Or <BR>\n" );
document.write( ".A piece of paper rolled into a cylinder widthwise<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 #772762 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=772762\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Rolling the cylinder lengthwise means that the circumference of the cylinder becomes the magnitude of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=width=W ALIGN=MIDDLE  ALT=\"width=W\"   DISABLED_style= \"max-width:90%; height:auto;\" >, and the height is the magnitude of the <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=length=L ALIGN=MIDDLE  ALT=\"length=L\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "so, if the circumference of the cylinder is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2Ar+=+W ALIGN=MIDDLE  ALT=\"2pi%2Ar+=+W\"   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=r+=+W%2F%282pi%29 ALIGN=MIDDLE  ALT=\"r+=+W%2F%282pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then the volume is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5B1%5D+=+pi%2Ar%5E2%2AL ALIGN=MIDDLE  ALT=\"V%5B1%5D+=+pi%2Ar%5E2%2AL\"   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=V%5B1%5D+=+pi%28W%2F%282pi%29%29%5E2%2AL ALIGN=MIDDLE  ALT=\"V%5B1%5D+=+pi%28W%2F%282pi%29%29%5E2%2AL\"   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=V+%5B1%5D=+pi%28W%5E2%2F%284%2Api%5E2%29%29L ALIGN=MIDDLE  ALT=\"V+%5B1%5D=+pi%28W%5E2%2F%284%2Api%5E2%29%29L\"   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=V%5B1%5D+=+%281%2F%284pi%29%29W%5E2%2AL ALIGN=MIDDLE  ALT=\"V%5B1%5D+=+%281%2F%284pi%29%29W%5E2%2AL\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "if the circumference of the cylinder is<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2pi%2Ar+=+L ALIGN=MIDDLE  ALT=\"2pi%2Ar+=+L\"   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=r+=+L%2F%282pi%29 ALIGN=MIDDLE  ALT=\"r+=+L%2F%282pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Then the volume is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5B2%5D+=+pi%2Ar%5E2%2AW ALIGN=MIDDLE  ALT=\"V%5B2%5D+=+pi%2Ar%5E2%2AW\"   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=V%5B2%5D+=+pi%28L%2F%282pi%29%29%5E2%2AW ALIGN=MIDDLE  ALT=\"V%5B2%5D+=+pi%28L%2F%282pi%29%29%5E2%2AW\"   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=V+%5B2%5D=+pi%28L%5E2%2F%284%2Api%5E2%29%29W ALIGN=MIDDLE  ALT=\"V+%5B2%5D=+pi%28L%5E2%2F%284%2Api%5E2%29%29W\"   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=V%5B2%5D+=+%281%2F%284pi%29%29L%5E2%2AW ALIGN=MIDDLE  ALT=\"V%5B2%5D+=+%281%2F%284pi%29%29L%5E2%2AW\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Dividing the width folding by the length folding:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F%284pi%29%29W%5E2%2AL+%2F+%281%2F%284pi%29%29L%5E2%2AW+=cross%28%281%2F4pi%29%29W%5Ecross%282%29%2Across%28L%29+%2F+cross%28%281%2F4pi%29%29L%5Ecross%282%29%2Across%28W%29+=W%2FL ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Thus the ratio of the two volumes is the ratio of the length to the width (interesting.) So the width folding has greater volume.\r<BR>\n" );
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