Question

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:

विकल्प

• 3 cm

• 2 cm

• 1.5 cm

• 2.5 cm

Answer 1

2 cm

Explanation:

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

\[\Rightarrow \frac{4}{3}\, \pi R^3 = 8 \times \frac{4}{3}\, \pi r^3\]

⇒ R³ = 8r³

⇒ R³ = 8 × 1³

⇒ R³ = 8

⇒ R³ = 2³

⇒ R = 2 cm.