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Three solid metallic spheres of diameter 6 cm, 8 cm and 10 cm are melted and recast into a new solid sphere. The diameter of the new sphere is :
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- 4 cm
- 6 cm
- 8 cm
- 12 cm
- 4 cm
Correct Option: D
According to the question, three solid metallic spheres are melted and recast into a new solid sphere. It means that the volume of new solid sphere will be equal to the sum of volume of three solid spheres.
| ∴ Volume of new solid sphere = | π |  |  | ³ | + | π | | | ³ | + | π | | | ³ | ||||||
| 3 | 2 | 3 | 2 | 3 | 2 |
| πr³ = | π [(3)³ + (4)³ + (5)³] | |||
| 3 | 3 |
= 27 + 64 + 125
⇒ r³ = 216
⇒ r³ = (6)³
⇒ r = 6 cm
∴ Diameter of the new sphere = 2 × 6 = 12 cm
