Eight metallic spheres, each of radius 2 cm, are melted and cast into a single sphere. Calculate the radius of the new (single) sphere.

Radius of metallic sphere (r) = 2 cm.

Volume of sphere = $\dfrac{4}{3}$πr³

∴ Volume of eight spheres (V) = 8 x $\dfrac{4}{3}$πr³

= $\dfrac{32}{3}$π(2)³

= $\dfrac{256}{3}$π cm³.

Since 8 spheres are combined to form a new bigger sphere,

∴ Volume of new sphere = V.

Let the radius of the big sphere be R cm.

$\therefore \dfrac{4}{3}πR^3 = \dfrac{256}{3}π \\[1em] \Rightarrow R^3 = \dfrac{256π}{3} \times \dfrac{3}{4π} \\[1em] \Rightarrow R^3 = 64 \\[1em] \Rightarrow R^3 = (4)^3 \\[1em] \Rightarrow R = 4 \text{ cm}.$

Hence, the radius of the new sphere = 4 cm.