Eight spheres of equal radii are obtained by melting a metallic sphere of radius 10 cm. Find the surface area of each sphere thus obtained.

Let the radius of small spheres formed be r₂

Radius of sphere which is melted = r₁ = 10 cm

As the sphere is melted and then the small spheres are made from the same amount of melted sphere, therefore, the volume remains same

8 small spheres are made

Volume of sphere = πr³

⇒ 8 × πr₂³ = πr₁³

⇒ 8r₂³ = r₁³

Substituting values

⇒ 8 × r₂³ = 10³

⇒ 8 × r₂³ = 1000

⇒ r₂³ =

⇒ r₂ = = 5 cm

Surface area of sphere = 4πr²

⇒ surface area of small spheres made = 4πr₂²

= 4 × π × 5²

= 4 × π × 25

= 100π cm²

Therefore, surface area of each sphere obtained is 100π cm²