Copper Cu wire

Copper wire with a diameter of 1 mm and a weight of 350 g is wound on a spool. Calculate its length if the copper density is p = 8.9 g/cm cubic.

Correct answer:

l =  5007 cm

Step-by-step explanation:

$$\begin{gathered} D=1\text{ mm}\to \text{ cm}=1\mathrm{/}10\text{ cm}=0.1\text{ cm } \\ m=350\text{ g } \\ \rho =8.9{\text{g/cm}}^3 \\ m=\rho V \\ V=m\mathrm{/}\rho =350\mathrm{/}8.9={\displaystyle \frac{3500}{89}}\doteq 39.3258{\text{cm}}^3 \\ r=D\mathrm{/}2=0.1\mathrm{/}2={\displaystyle \frac{1}{20}}=0.05\text{ cm } \\ S=\pi \cdot r^2=3.1416\cdot 0.05^2\doteq 0.0079{\text{cm}}^2 \\ V=Sl \\ l=V\mathrm{/}S=39.3258\mathrm{/}0.0079=5007\text{ cm} \end{gathered}$$

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