A copper sphere having a radius of 6 cm is melted and then drawn into a cylindrical wire of radius 2 mm. Calculate the length of the wire.

Let the length of the wire be h cm

Radius of the sphere, R = 6 cm

Radius of the wire, r = 2 mm = 0.2 cm

Given, copper sphere is melted into wire.

∴ Volume of the wire = Volume of the sphere

$\Rightarrow π\text{r}^2 \text{h} = \dfrac{4}{3}π\text{R}^3 \\[1em] \Rightarrow \text{r}^2 \text{h} = \dfrac{4}{3}\text{R}^3 \\[1em] \Rightarrow 0.2^2 \times \text{h} = \dfrac{4}{3} \times 6^3 \\[1em] \Rightarrow 0.04 \times \text{h} = \dfrac{4}{3} \times 216 \\[1em] \Rightarrow \text{h} = \dfrac{4 \times 216}{3 \times 0.04} \\[1em] \Rightarrow \text{h} = \dfrac{864}{0.12} \\[1em] \Rightarrow \text{h} = 7200 \text{ cm.} \\[1em] \Rightarrow \text{h} = 72 \text{ m}.$

Hence, the length of the wire is 72 m.