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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?

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? Correct Answer 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

⇒ 216 = 91 + r3

⇒ 216 - 91 = r3

⇒ r3 = 125 

⇒ r = ∛125

⇒ r = 5 

∴ Radius of third small sphere is 5 cm

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