If a metallic cube of edge 1 cm is drawn into a wire of diameter 4 mm, then the length of the

wire is :

Suppose the length of wire formed is h.
Each edge of metallic cube = 1 cm = 10 mm
So volume of metallic cube = ${\left(10\right)}^3 {\mathrm{mm}}^3$ = 1000 ${\mathrm{mm}}^3$
Now diameter of wire formed = 4 mm
Then its radius; r = $\frac{4}{2}$ = 2 mm
Since the metallic cube is drawn in to wire, so we have;
Volume of metallic cube = volume of wire
$$\begin{gathered} \Rightarrow 1000 = {\mathrm{\pi r}}^2\mathrm{h} \\ \Rightarrow 1000 = \frac{22}{7}\times 2^2\times \mathrm{h} \\ \Rightarrow 1000 = \frac{88\mathrm{h}}{7} \\ \Rightarrow \mathrm{h} = \frac{1000\times 7}{88} = 79.545 \end{gathered}$$
Therefore the length of the wire is 79.545 mm.