A solid metallic sphere of radius 8 cm is melted and recast into spherical balls each of radius 2 cm.

We have,

Radius of the solid metallic sphere, $R=8 \mathrm{~cm}$ and

Radius of the spherical ball, $r=2 \mathrm{~cm}$

Now,

The number spherical balls obtained $=\frac{\text { Volume of the solid metallic sphere }}{\text { Volume of a spherical ball }}$

$=\frac{\left(\frac{4}{3} \pi R^{3}\right)}{\left(\frac{4}{3} \pi r^{3}\right)}$

$=\left(\frac{R}{r}\right)^{3}$

$=\left(\frac{8}{2}\right)^{3}$

$=4^{3}$

$=64$

So, the number of spherical balls obtained is 64.