• # Question: say you put a rubber band around the earth and then made it longer by a metre what would happen?

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Asked by lilpump to Xu, Kathryn, Ian, Hina on 13 Jun 2018.
• Ian Jones answered on 13 Jun 2018:

The circumference of a circle is pi*D so if you made the circumference 1m longer the diameter would be 1m / pi bigger. 1/3.14159 is about 32cm.

That’s the diameter. So the increase in radius would be about 16cm.

Interestingly, the same is true however large or small the circle is! So if you had an infinitely small circle and increased the circumference by 1m, the radius would also be 16cm!

Isn’t that odd!!?

• Kathryn Burrows answered on 13 Jun 2018:

It would be quite an engineering achievement to put a rubber band around the Earth! I would not be surprised if increasing the length caused it to snap! Rubber bands only stretch so far! The Earth is actually more like a squashed circle and the rubber band would dip down into the ocean unless you balanced it on boats. Ian has already given the most sensible answer though, modelling the Earth as a sphere you get Length = 2*pi*radius, L^{old}=2*pi*r^{old}; L^{new}=2*pi*r^{new}; L^{new}=L^{old}+1 such that r^{new}-r^{old}=1/(2*pi) = approximately 16 cm.