Eight identical metallic spheres, each of radius 1 cm are melted and recast into a solid sphere. The radius of the solid sphere formed is :

1. 3 cm

2. 2 cm

3. 1.5 cm

4. 2.5 cm

Given,

Radius of small metallic sphere (r) = 1 cm

Eight identical metallic spheres, each of radius 1 cm are melted and recast into a solid sphere.

Let radius of solid sphere formed be R.

∴ Volume of large metallic sphere = 8 × Volume of each smaller sphere

$\Rightarrow \dfrac{4}{3}πR^3 = 8 \times \dfrac{4}{3}πr^3 \\[1em] \Rightarrow R^3 = 8r^3 \\[1em] \Rightarrow R^3 = 8 \times 1^3 \\[1em] \Rightarrow R^3 = 8 \\[1em] \Rightarrow R^3 = 2^3 \\[1em] \Rightarrow R = 2 \text{ cm}.$

Hence, Option 2 is the correct option.