Sentences like this always bother me. Of what use is this information? Barbed wire isn't used as a counterweight. How much fence is 3 million pounds?
Probably something like 9,000 miles[1]
Of many metrics, the length might not be that interesting. For instance how much land did that represent making safe for crops, and conversely how much territory was ruined for grazing?
While there isn't demand for barbed wire for as a counterweight, it does add some context on the supply side. The 173 m^3 of steel is about 0.3% of the steel used to construct the Three Gorges Dam, and 20% of the steel used to construct the Eiffel Tower[2]
[1] Wolfram|Alpha seems to change the syntax handling from month to month, but for now using weight/density of steel treats it like a physical object unlike "volume of steel" which returns market trading volumes.
http://www.wolframalpha.com/input/?i=%283e6+lbs+%2F+density+...
So 3 million lbs would be 9375 miles, or 15000km
I also guess that many nail manufacturers produced barbed wire.