Correct Answer – Option 1 : 5 cm

Given :-

Spherical ball of radius 6 cm

Recast into three spherical ball having radius = 3 cm and 4 cm 

Concept :-

Volume of sphere = (4/3)πR³

Volume of spherical ball = Summation of volume of small spherical balls

Calculation :- 

Let radius of small spheres are r₁ , r₂ and r₃

r₁ = 3 cm and r₂ = 4 cm

Volume of sphere ball = Volume of first sphere + Volume of second sphere + Volume of third sphere

⇒ (4/3) × π × 6³ = (4/3) × π × 3³ + (4/3) × π × 4³ + (4/3) × π × (r)³

⇒ (4/3) × π × 216 = (4/3) × π [27 + 64 + r³]

⇒ 216 = 91 + r³

⇒ 216 – 91 = r³

⇒ r³ = 125 

⇒ r = ∛125

⇒ r = 5 

∴ Radius of third small sphere is 5 cm