Question

The diameter of a copper sphere is 6 cm. It is melted and drawn into a long wire of uniform circular cross-section. If the length of the wire is 36 cm, find its radius.

Answer 1

Diameter of the sphere = 6 cm
So, radius of the sphere = 3 cm
Volume of the sphere = $\frac{4}{3}\mathrm{\pi }{r}^3$
$$\begin{gathered} =\frac{4}{3}\times \frac{22}{7}\times 3\times 3\times 3 \\ =\frac{792}{7}{\mathrm{cm}}^3 \end{gathered}$$
Length of the wire = 36 cm
Since, the sphere is melted and drawn into a wire, the volume of the sphere is equal to the wire.
Volume of the wire = $\frac{792}{7}{\mathrm{cm}}^3$
$$\begin{gathered} \Rightarrow \mathrm{\pi }{r}^{2}h=\frac{792}{7} \\ \Rightarrow r^2=\frac{792}{7\times \mathrm{\pi }h} \\ \Rightarrow r^2=\frac{792\times 7}{7\times 22\times 36} \\ \Rightarrow r^2=1 \\ \Rightarrow r=1\mathrm{cm} \end{gathered}$$