Question 117415
The diameter of the wire is 2 mm
1 mm = .001 m
2 mm = .002 m
The cross-section area of the wire is
{{{A = pi*r^2}}}
{{{A = pi*.001^2}}}
{{{A = 3.1416*10^-6}}}
The volume of the wire is
{{{A*L}}} where L is the length
Since a known volume has a known weight, 
I can set up a proportion
6.8 g / 1 cm3 = 1200 g / V
1 cm3 = .0001 m3
{{{6.8 / 10^-4 = 1.2*10^3 / V}}}
multiply both sides by V
{{{6.8V / 10^-4 = 1.2*10^3}}}
multiply both sides by 10^-4
{{{6.8V = 1.2*10^3*10^-4}}}
divide both sides by 6.8
{{{V = 1.2*10^-1 / 6.8}}}
{{{V = .017647}}}
{{{V = A*L}}}
{{{L = V / A}}}
{{{L = 1.7647*10^-2 / (3.1416*10^-6)}}}
{{{L = (1.7647 / 3.1416)*10^4}}}
{{{L = .5617*10^4}}}
{{{L = 5.617*10^3}}}m
The length to the nearest meter is 5,617 m
check answer
{{{6.8 / 10^-4 = 1.2*10^3 / V}}}
{{{6.8 / 10^-4 = 1.2*10^3 / (A*L)}}}
{{{6.8 / 10^-4 = 1.2*10^3 / (3.14159*10^-6*5.617*10^3)}}}
{{{6.8*10^4 = 1.2*10^6 / (3.14159*5.617)}}}
{{{6.8*10^4 = 1.2*10^6 / 1.7646*10^1}}}
{{{6.8*10^4 = .68004*10^5}}}
{{{6.8 = 6.8004}}}
close enough