Question

Find the length of 13.2 kg of copper wire of diameter 4 mm, when 1 cubic centimetre of copper weighs 8.4 g.

Answer 1

Mass of copper wire = 13.2 kg = 13.2 × 1000 = 13200 g (1 kg = 1000 g)

Volume of 8.4 g of copper wire = 1 cm³

∴ Volume of 13200 g (or 13.2 kg) of copper wire = $\frac{13200}{8.4}$ cm³

Let the length of the copper wire be l cm.

Radius of the copper wire, r = $\frac{4}{2}$ = 2 mm = 0.2 cm (1 cm = 10 mm)

∴ Volume of the copper wire = $\mathrm{\pi }{r}^{2}l=\frac{22}{7}\times {\left(0.2\right)}^2\times l$ cm<sup>3

$$\begin{gathered} \Rightarrow \frac{22}{7}\times {\left(0.2\right)}^2\times l=\frac{13200}{8.4} \\ \Rightarrow l=\frac{13200\times 7}{22\times {\left(0.2\right)}^2\times 8.4} \\ \Rightarrow l=12500\mathrm{cm} \end{gathered}$$</sup>

$$\begin{gathered} \Rightarrow l=\frac{12500}{100}\left(1\mathrm{m}=100\mathrm{cm}\right) \\ \Rightarrow l=125\mathrm{m} \end{gathered}$$
Thus, the length of the copper wire is 125 m.