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# How much more string is required which wrapped around the equator (40k km) is made to expand 15cms?

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How much more string is required which wrapped around the equator (40k km) is made to expand 15cms?

If a piece of string is wrapped around the earth’s equator (40k kms) is made to expand such that it now hovers 15cm above the equator how much more thread is needed?

1) 1 meter 2). 1km or 3). 10k kms

The trick here is to understand that no matter what the size of the circle i.e. the circumference of the earth, as is in this example or a tennis ball for that matter when the circumference increases by 15cms the length of the string will expand by the same amount each time.

Strictly mathematically speaking the circumference of the circle will increase by 2*π*radius. If the thread expands such that it now hovers 15 cms over the equator of the earth the additional thread required will be 15*22/7*2 = 94cms or almost 1 metre.

What’s really interesting to note is that regardless of the thread being wrapped around a tennis ball or the circumference of the earth, the rope will always increase ~1 metre in size if the radius increases by 15cms.

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