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? Please round to the nearest gram.

Correct answer:

m =  2121 g

Step-by-step explanation:

$$\begin{gathered} l=250\text{m}\to \text{cm}=250\cdot 100\text{cm}=25000\text{cm} \\ D=2\text{mm}\to \text{cm}=2:10\text{cm}=0.2\text{cm} \\ \rho =2700{\text{kg/m}}^3\to {\text{g/cm}}^3=2700:1000{\text{g/cm}}^3=2.7{\text{g/cm}}^3 \\ r=D/2=0.2/2=\frac{1}{10}=0.1\text{cm} \\ S=\pi \cdot r^2=3.1416\cdot 0.1^2\doteq 0.0314{\text{cm}}^2 \\ V=S\cdot l=0.0314\cdot 25000\doteq 785.3982{\text{cm}}^3 \\ m=\rho \cdot V=2.7\cdot 785.3982=2121\text{g} \end{gathered}$$

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