Math CentralQuandaries & Queries


Question from Terry:

I heard this on T.V. and was wondering if it was true. Place a string around the world, you would need 25,000 miles of string. If you raised the string off of the ground by 1 foot all the way around. How much more string
would you need?

Hi Terry,

The circumference of a circle is 2π × r where r is the radius. I want to work in feet so using your number of 25,000 miles the circumference of the earth in feet is

25,000 × 5,280 = 2π × r


r = 25,000 × 5,280/2π feet.

If the radius is increased by 1 foot the new circumference is

new circumference = 2π × (r + 1)

Use the value of r obtained above, calculate the new circumference and compare it to 25,000 × 5,280.


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