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A solid metallic spherical ball of radius 4 cm recast into three solid metallic spherical balls whose radii are 2 cm, 3 cm and x cm, find the value of x.

A solid metallic spherical ball of radius 4 cm recast into three solid metallic spherical balls whose radii are 2 cm, 3 cm and x cm, find the value of x. Correct Answer ∛29

As we know,

Volume of sphere = (4/3) × π r3

Radius of bigger ball R = 4

Volume of bigger ball = (4/3) × π × 43

Radius of smaller balls is 2 cm, 3 cm and x cm.

Volume of all three smaller balls = (4/3) × π × (23 + 33 + x3)

According to the question

Volume of bigger ball = Volume of all three smaller balls

⇒ (4/3) × π × 43 = (4/3) × π × (23 + 33 + x3)

⇒ 64 = 8 + 27 + x3

⇒ x3 = 64 – 35 = 29

⇒ x = ∛29

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