## Task 2 - V10812

At the VEB Kabelwerk Köpenick, a wire with a diameter of $6 \mathrm{~mm}$ and a length of $4 \mathrm{~m}$ is drawn into a wire with a diameter of $0.02 \mathrm{~mm}$.

How long is this wire?
The volume of the wire remains constant, i.e.,

$$
\pi r_{a}^{2} l_{a}=\pi r_{e}^{2} l_{e} \Rightarrow l_{e}=\frac{r_{a}^{2}}{r_{e}^{2}} \cdot l_{a}
$$

where $r_{a}, l_{a}$ are the radius and length at the beginning, and $r_{e}, l_{e}$ are the radius and length of the final product. Substituting the values gives $l_{e}=360$ million $\mathrm{mm}=360 \mathrm{~km}$.