Question

The radius of a metallic sphere is 9 cm. It was melted to make a wire of diameter 4 mm. Find the length of the wire.

Answer 1

Radius of the sphere, R = 9 cm

Radius of the wire, r = $\frac{4}{2}$ = 2 mm = $\frac{2}{10}$ = 0.2 cm (1 cm = 10 mm)

Let the length of the wire be l cm.

It is given that the metallic sphere is melted to make the wire.

∴ Volume of metal in the wire = Volume of the metallic sphere

$$\begin{gathered} \Rightarrow \mathrm{\pi }{r}^{2}l=\frac{4}{3}\mathrm{\pi }{R}^3 \\ \Rightarrow l=\frac{{\displaystyle \frac{4}{3}}{R}^3}{r^2} \\ \Rightarrow l=\frac{{\displaystyle \frac{4}{3}}\times {\left(9\right)}^3}{{\left(0.2\right)}^2} \\ \Rightarrow l=24300\mathrm{cm} \end{gathered}$$
$$\begin{gathered} \Rightarrow l=\frac{24300}{100} \\ \Rightarrow l=243\mathrm{m}\left(1\mathrm{m}=100\mathrm{cm}\right) \end{gathered}$$
Thus, the length of the wire is 243 m.