Copper wire meters

How many meters of copper wire with a diameter of d=3 mm will be produced from 60 kg of copper scrap if the specific gravity of copper is p=9 g/cm³?

Final Answer:

l =  943.1404 m

Step-by-step explanation:

$$\begin{gathered} d=3\text{mm}\to \text{cm}=3:10\text{cm}=0.3\text{cm} \\ m=60\text{kg}\to \text{g}=60\cdot 1000\text{g}=60000\text{g} \\ \rho =9{\text{g/cm}}^3 \\ m=\rho V \\ V=m/\rho =60000/9=\frac{20000}{3}\doteq 6666.6667{\text{cm}}^3 \\ r=d/2=0.3/2=\frac{3}{20}=0.15\text{cm} \\ S=\pi \cdot r^2=3.1416\cdot 0.15^2\doteq 0.0707{\text{cm}}^2 \\ V=S\cdot l \\ L=V/S=6666.6667/0.0707\doteq 94314.0404\text{cm} \\ l=L\to \text{m}=L:100\text{m}=94314.0404:100\text{m}=943.14\text{m}=943.1404\text{m} \end{gathered}$$

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