## 81. Math Puzzle $2 / 72$

On a wooden roll with a diameter of $10 \mathrm{~cm}$, a long paper strip is tightly wound and together with the wooden roll forms a cylinder with a diameter of $30 \mathrm{~cm}$.

How long is the wound paper strip approximately, if the paper is $0.1 \mathrm{~mm}$ thick, no air gap was left between the layers, and the beginning and end of the strip lie on the same radius (through the central axis of the cylinder)?
The wrapped paper represents a hollow cylinder with a wall thickness of $10 \mathrm{~cm}$; thus, $\frac{100}{0.1}=1000$ layers are wound up.

The layers have an average length of $r_{\text {Middle }} \cdot 2 \pi=\frac{5+15}{2} \cdot 2 \pi=20 \pi \mathrm{cm}$.

The total wound length is $L=1000 \cdot 20 \pi \approx 628 \mathrm{~cm}$.