Question

A copper rod of diameter 1 cm and length 8 cm is drawn into a wire of length 18 m of uniform thickness. Find the thickness of the wire.

Answer 1

The radius of the copper rod is 0.5 cm and length is 8 cm. Therefore, the volume of the copper rod is

Let the radius of the wire is r cm. The length of the wire is 18 m=1800 cm. Therefore, the volume of the wire is

Since, the volume of the copper rod is equal to the volume of the wire; we have

$$\begin{gathered} V_1=V \\ \Rightarrow \mathrm{\pi }{r}^2\times 1800=\mathrm{\pi }\times {\left(0.5\right)}^2\times 8 \\ \Rightarrow r^2=\frac{0.25\times 8}{1800}=\frac{1}{900} \\ \Rightarrow r=\frac{1}{30}=0.033\mathrm{cm} \end{gathered}$$

Hence, the radius of the wire is 0.033 cm = 0.33 mm.
So, thickness = $0.33\times 2=0.66\mathrm{mm}$