Question

A copper sphere of diameter 18 cm is drawn into a wire of diameter 4 mm. Find the length of the wire.

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{Radius}\mathrm{of}\mathrm{the}\mathrm{sphere},R=\frac{18}{2}=9\mathrm{cm}\mathrm{and} \\ \mathrm{Radius}\mathrm{of}\mathrm{the}\mathrm{wire},r=\frac{4}{2}=2\mathrm{mm}=0.2\mathrm{cm} \\ \mathrm{Let}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{wire}\mathrm{be}l. \\ \mathrm{Now}, \\ \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{wire}=\mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{copper}\mathrm{sphere} \\ \Rightarrow \mathrm{\pi }{r}^{2}l=\frac{4}{3}\mathrm{\pi }{R}^3 \\ \Rightarrow l=\frac{4R^3}{3r^2} \\ \Rightarrow l=\frac{4\times 9\times 9\times 9}{3\times 0.2\times 0.2} \\ \therefore l=24300\mathrm{cm}=243\mathrm{m} \end{gathered}$$

So, the length of the wire is 243 m.