A sphere having a radius of 3 cm is melted and elongated into a wire having a circular cross-section of a radius of 0.1 cm. Find the length of the wire.

Given: Radius of the sphere (R) = 3 cm

The radius of the circular wire (r) = 0.1 cm

Let the length of the wire be h.

It is known that the volume of solids remains the same in case of the conversion of solids from one shape into another.

∴ Volume of circular wire = Volume of the sphere

$\Rightarrow {\mathrm{\pi r}}^2\mathrm{h}=\frac{4}{3}{\mathrm{\pi R}}^3$
$\Rightarrow 0.1^2\times \mathrm{h}=\frac{4}{3}\times {\left(3\right)}^3$

$\Rightarrow \mathrm{h}=\frac{36}{0.01}$

$\Rightarrow \mathrm{h}=3600 \mathrm{cm}$

$\Rightarrow \mathrm{h}=36 \mathrm{m}$

Therefore, the length of the wire is 36 m.