A metallic sphere of radius 12 cm is melted into three smaller

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A metallic sphere of radius 12 cm is melted into three smaller spheres. If the radii of two smaller spheres are 6 cm and 8 cm, the radius of the third is ?

1. 14 cm
2. 16 cm
3. 10 cm
4. 12 cm

Correct Option: C

Let radius of the third sphere be r.
Then, 4/3 π x (12)³ = 4/3 π x (6)³ + 4/3π x (8)³ + 4/3 πr³
⇒ (12)³ = (6)³ + (8)³ + r³
⇒ r³ = 1728 - 216 - 512
⇒ r³ = 1000
∴ r = 10 cm