A solid lead ball of radius 6 cm is melted and then drawn into a wire of diameter 0.2 cm. Find the length of the wire.

Let h be the length of the wire.

Here, the volume of the lead ball = volume of the wire (i.e. cylindrical wire)

$\frac{4}{3}{\mathrm{\pi r}}^3={\mathrm{\pi r}}^2\mathrm{h}$

$\Rightarrow \frac{4}{3}\mathrm{\pi }\times {\left(6\right)}^3=\mathrm{\pi }\times {\left(0.1\right)}^2\times \mathrm{h}$

$\Rightarrow \mathrm{h}=\frac{4\times 216}{3\times 0.01}=28800 \mathrm{cm}$

$\Rightarrow \mathrm{h}= 288 \mathrm{m}$

Hence, the length of the wire = 288 m