document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=79682>Question 79682</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The Rope Around the Earth Puzzle: Imagine a rope tied around the Earth’s equator like a ring on a person’s finger.  Now imagine lifting off this very long rope, cutting it somewhere so as to stitch into it exactly one meter of extra rope.  Then imagine placing this longer rope back around the Earth at the equator.  Since it is longer than the original rope by just one meter, a gap between the rope and the Earth’s surface will form all the way around.  How large is the gap that is formed? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #57182 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=57182\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The Rope Around the Earth Puzzle: Imagine a rope tied around the Earth’s equator like a ring on a person’s finger.  Now imagine lifting off this very long rope, cutting it somewhere so as to stitch into it exactly one meter of extra rope.  Then imagine placing this longer rope back around the Earth at the equator.  Since it is longer than the original rope by just one meter, a gap between the rope and the Earth’s surface will form all the way around.  How large is the gap that is formed?<BR>\n" );
document.write( "-----------<BR>\n" );
document.write( "The 1st rope has circumference  C=(pi)d<BR>\n" );
document.write( "So d = C/pi<BR>\n" );
document.write( "-------------<BR>\n" );
document.write( "After adding a meter you <BR>\n" );
document.write( "C+1 = (pi)d+1<BR>\n" );
document.write( "C+1 = pi[d+1/pi]<BR>\n" );
document.write( "So the diameter of the new rope is [d+1/pi] meters<BR>\n" );
document.write( "This new diameter is 1/pi  m longer<BR>\n" );
document.write( "So the new radius is 1/2pi m longer<BR>\n" );
document.write( "So the gap is 1/2pi meter<BR>\n" );
document.write( "=========<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
document.write( "\n" );
document.write( "  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );