Putting a Ribbon around the EarthDate: 12/23/2006 at 16:38:46 From: Tim Subject: circumference of the earth If a ribbon around the circumference of the earth is 24900 miles, and we wanted a ribbon to be 1 inch above the surface, what would be the length of the extra ribbon we would need? I was told all you had to do to find the answer is take the 1 inch times 2 times 3.14 = 6.28 inches. If this is correct then the same length would add 1 inch the the circumference of a basketball. Are you starting to scratch your head, too?? Date: 12/23/2006 at 22:18:07 From: Doctor Rich Subject: Re: circumference of the earth Hello Tim, Thank you for contacting the Math Forum. Your question is a fairly well known one, because the results seem hard to believe. But it really is true. Let's look at why. Assuming that the earth is a perfect sphere, we would have a circle with a circumference of 24,900 miles at the equator. That means the radius would be 24,900/(2*pi) or about 3963 miles. What if we think of the loose ribbon as a second circle around the earth with a radius that is 1 inch longer than the radius of the earth? Ribbon * * * * * * * * * * * * Earth * * r + 1 inch * * x-----------*-* * * * * * * * * * * * * * * The circumference of a circle C with radius (r) is C = 2 Pi(r) The circumference of a circle C with radius (r + 1) is C = 2 Pi(r+1) C = 2 Pi(r) + 2 Pi From this you can see that the circumference will increase by 2Pi. In this problem, since the radius increases by 1 inch, then your answer of a 6.28 inch increase in the length of the ribbon is correct. Note that no matter what the original radius is (the radius of the earth or the radius of a basketball), increasing it by 1 inch will always lead to an increase of 2Pi or 6.28 inches in the circumference. I think part of what's so hard to believe about this problem is that when we think about the circumference of the earth, we assume it has to be some really large number, especially in comparison to the basketball. But as the math shows, you'll get the same answer for any size original radius! I hope that helps solve your dilemma. Please contact me if I can be of further assistance. - Doctor Rich, The Math Forum http://mathforum.org/dr.math/ |
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