Question

1 cm³ of gold is drawn into a wire 0.1 mm in diameter. Find the length of the wire.

Answer 1

Let r cm be the radius of the wire and h cm be the height of the wire.
Volume of the gold = 1 cm³
1 cm³ of gold is drawn into a wire of diameter 0.1 mm.
Here, r = $0.1\mathrm{mm}=\frac{0.1}{20}\mathrm{cm}=\frac{1}{200}\mathrm{cm}$
$$\begin{gathered} \therefore \mathrm{\pi }{r}^{\mathit{2}}h=1 \\ \Rightarrow \frac{22}{7}\times \frac{1}{200}\times \frac{1}{200}\times h=1 \\ \Rightarrow h=\frac{40000\times 7}{22}=12727.27\mathrm{cm} \end{gathered}$$

Hence, length of the wire = 127.27 m