Math CentralQuandaries & Queries


Question from Tammy, a parent:

My 9 year old son asked me a question and I have no idea how to work it out! Please can you help?

If the earth was made of a ball of string and you unravelled the string how long would it be? Assuming the string is 5mm thick.

Hi Tammy,

I think that the person who asked the questions wants your son to assume that the volume of the length of string would be the same as the volume of the earth. The string is a long circular cylinder with radius $\large \frac52\normalsize \mbox{ mm }$ and unknown length. The volume of a circular cylinder is $\pi\; r^2 l$ where $l$ is the length. The earth is approximately a sphere and the volume of a sphere is $\large \frac43 \normalsize \pi \; r^3$ where $r$ is the radius of the sphere.

I suggest that you convert the $2.5 \mbox{ mm }$ radius of the string to meters, look up the radius of the earth in meters, equate two volumes and solve for $l$ in meters.

I hope this helps,


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