Wire weight

The customer wants to buy 300 meters of wire with d = 4 mm. An experienced salesman knows that 100 meters of wire are about 10 kilograms, so he weighs 30 kilograms of wire. Find out how many meters of wire are in a bundle of wire weighing 30 kilograms (or there will be about 300 meters) if one cubic meter of wire weighs 7800 kilograms.

Final Answer:

x =  306.0672 m

Step-by-step explanation:

$$\begin{gathered} \rho =7800{\text{kg/m}}^3 \\ d=4\text{mm}\to \text{m}=4:1000\text{m}=0.004\text{m} \\ r=d/2=0.004/2=\frac{1}{500}=0.002\text{m} \\ m=30\text{kg} \\ x=\frac{m}{\rho \cdot \pi \cdot r^2}=\frac{30}{7800\cdot 3.1416\cdot 0.002^2}=306.0672\text{m} \end{gathered}$$

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