# The copper wire

The copper wire bundle with a diameter of 2.8mm has a weight of 5kg. How many meters of wire is bundled if 1m3 of copper weighs 8930kg?

Result

l =  90.9 m

#### Solution:

$D=2.8 \ \text{mm} \ \\ m=5 \ \text{kg} \ \\ ρ=8930 \ \text{kg/m}^3 \ \\ \ \\ r=D/2=2.8/2=\dfrac{ 7 }{ 5 }=1.4 \ \text{mm} \ \\ r_{2}=r \rightarrow m=r / 1000 \ m=1.4 / 1000 \ m=0.0014 \ m \ \\ S=\pi \cdot \ r_{2}^2=3.1416 \cdot \ 0.0014^2 \doteq 0 \ \text{m}^2 \ \\ \ \\ m=ρV \ \\ m=ρ S l \ \\ \ \\ l=\dfrac{ m }{ ρ \cdot \ S } \ \\ l=\dfrac{ m }{ ρ \cdot \ \pi \cdot \ r_{2}^2 }=\dfrac{ 5 }{ 8930 \cdot \ 3.1416 \cdot \ 0.0014^2 } \doteq 90.9311 \doteq 90.9 \ \text{m}$

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