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 =  2121 g

Solution:

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

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