Question

66 cubic cm of silver is drawn into a wire 1 mm in diameter. Calculate the length of the wire in metres.

Answer 1

$$\begin{gathered} \mathrm{We}\mathrm{have}, \\ \mathrm{Radius}\mathrm{of}\mathrm{wire},r=\frac{1}{2}=0.5\mathrm{mm}=0.05\mathrm{cm} \\ \mathrm{Let}\mathrm{the}\mathrm{length}\mathrm{of}\mathrm{the}\mathrm{wire}\mathrm{be}l. \\ \mathrm{As}, \\ \mathrm{Volume}\mathrm{of}\mathrm{the}\mathrm{wire}=66{\mathrm{cm}}^3 \\ \Rightarrow \mathrm{\pi }{r}^{2}l=66 \\ \Rightarrow \frac{22}{7}\times 0.05\times 0.05\times l=66 \\ \Rightarrow l=66\times \frac{7}{22\times 0.05\times 0.05} \\ \therefore l=8400\mathrm{cm}=84\mathrm{m} \end{gathered}$$

So, the length of the wire is 84 m.