AL wire

What is the weight of an aluminum wire 250 m long with a diameter of 2 mm, if the density of aluminum is p = 2700 kg/m cubic. Determine to the nearest gram.

Correct result:

m =  21 g

Solution:

l=250 m D=2 mm→cm=2/10 cm=0.2 cm ρ=2700 kg/m3→g/cm3=2700/1000 g/cm3=2.7 g/cm3  r=D/2=0.2/2=110=0.1 cm S=π⋅ r2=3.1416⋅ 0.12≐0.0314 cm2 V=S⋅ l=0.0314⋅ 250≐7.854 cm3  m=ρ⋅ V=2.7⋅ 7.854=21 gl=250 \ \text{m} \ \\ D=2 \ mm \rightarrow cm=2 / 10 \ cm=0.2 \ cm \ \\ ρ=2700 \ kg/m^3 \rightarrow g/cm^3=2700 / 1000 \ g/cm^3=2.7 \ g/cm^3 \ \\ \ \\ r=D/2=0.2/2=\dfrac{ 1 }{ 10 }=0.1 \ \text{cm} \ \\ S=\pi \cdot \ r^2=3.1416 \cdot \ 0.1^2 \doteq 0.0314 \ \text{cm}^2 \ \\ V=S \cdot \ l=0.0314 \cdot \ 250 \doteq 7.854 \ \text{cm}^3 \ \\ \ \\ m=ρ \cdot \ V=2.7 \cdot \ 7.854=21 \ \text{g}

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