A spherical ball of lead 6 cm in radius is melted and recast into thre

1.	A spherical ball of lead 6 cm in radius is melted and recast into three spherical balls. The radii of two of ball are 3 cm and 4 cm. What is the radius of third sphere?1. 5 cm2. 5.5 cm3. 6 cm4. 6.6 cm
Answer» 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

A spherical ball of lead 6 cm in radius is melted and recast into three spherical balls. The radii of two of ball are 3 cm and 4 cm. What is the radius of third sphere?1. 5 cm2. 5.5 cm3. 6 cm4. 6.6 cm

Answer» 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

Discussion

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