Copper wire

What is the mass of 500 m of copper wire with a diameter of 1 mm, if ρ = 8.9 g/cm ^ 3?

Correct answer:

m =  3.495 kg

Step-by-step explanation:

$$\begin{gathered} l=500\text{ m}\to \text{ cm}=500\cdot 100\text{ cm}=50000\text{ cm } \\ D=1\text{ mm}\to \text{ cm}=1\mathrm{/}10\text{ cm}=0.1\text{ cm } \\ r=D\mathrm{/}2=0.1\mathrm{/}2={\displaystyle \frac{1}{20}}=0.05\text{ cm } \\ p=8.9{\text{g/cm}}^3 \\ V=\pi \cdot r^2\cdot l=3.1416\cdot 0.05^2\cdot 50000\doteq 392.6991{\text{cm}}^3 \\ {m}_1=p\cdot V=8.9\cdot 392.6991\doteq 3495.0218\text{ g } \\ m=m_1\to \text{ kg}=m_1\mathrm{/}1000\text{ kg}=3495.0218\mathrm{/}1000\text{ kg}=3.495\text{ kg}=3.495\text{ kg} \end{gathered}$$

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