This problem asks you to use your knowledge of cylinders to calculate the length of a roll of paper. In order to solve this problem use the fact that the volume of the paper will be the same in both the cylinder and as a flat sheet.

$$
\(\begin{aligned}
& \text { volume of cylinder }=\text { volume of sheet } \\
& \text { height } \cdot \pi r^2=\text { height } \cdot \text { length } \cdot \text { thickness }
\end{aligned}\)
$$


Now plug in the values given in the problem:

$$
\(\begin{aligned}
1 m \cdot \pi(.5 m)^2 & =1 \mathrm{~m} \cdot \text { length } \cdot .2 \mathrm{~mm} & & \text { Substitution } \\
1 m \cdot \pi(.5 \mathrm{~m})^2 & =1 \mathrm{~m} \cdot \text { length } \cdot .0002 \mathrm{~m} & & \text { Convert to common units } \\
\frac{1 m \cdot \pi(.5 \mathrm{~m})^2}{1 m \cdot .0002 m} & =\text { length } & & \text { Isolate the variable } \\
3926.99 \mathrm{~m} & =\text { length } & & \text { Calculate }
\end{aligned}\)
$$


The answer rounds to $\(3,927 \mathrm{~m}\)$. The correct answer choice is $\(\mathbf{D}\)$.