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.
\( volume of cylinder = volume of sheet height ⋅πr2= height ⋅ length ⋅ thickness \)
Now plug in the values given in the problem:
\(1m⋅π(.5m)2=1 m⋅ length ⋅.2 mm Substitution 1m⋅π(.5 m)2=1 m⋅ length ⋅.0002 m Convert to common units 1m⋅π(.5 m)21m⋅.0002m= length Isolate the variable 3926.99 m= length Calculate \)
The answer rounds to $
3,927 m$. The correct answer choice is $
D$.