Question

The diameter of a sphere is 42 cm. It is melted and drawn into a cylindrical wire of diameter 2.8 cm. Find the length of the wire.

Answer 1

Diameter of sphere = 42 cm
Radius of sphere = 21 cm

Volume of sphere$=\frac{4}{3}{\mathrm{\pi r}}^3=\frac{4}{3}\mathrm{\pi }\times 21\times 21\times 21{\mathrm{cm}}^3$

Diameter of wire = 2.8 cm
Radius of wire = 1.4 cm
Let the length of the wire be l cm.
Volume of the wire$={\mathrm{\pi r}}^2\mathrm{l}=\mathrm{\pi }\times 1.4\times 1.4\times \mathrm{l}$

The volume of the sphere is equal to the volume of the wire.
​Therefore,
$$\begin{gathered} \mathrm{\pi }\times 1.4\times 1.4\times l=\frac{4}{3}\mathrm{\pi }\times 21\times 21\times 21 \\ l=\frac{4\times 21\times 21\times 21}{3\times 1.4\times 1.4}=6300\mathrm{cm}=63\mathrm{m} \end{gathered}$$

So, the wire is 63 m long.