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,

Penny