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By melting two solid metallic spheres of radii 1 cm and 6 cm, a hollow sphere of thickness 1 cm is made. The external radius of the hollow sphere will be
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- 9 cm
- 6 cm
- 7 cm
- 8 cm
- 9 cm
Correct Option: A
| Volume of two solid metallic spheres = | π(r1³ + r2³) | |
| 3 |
| = | (1³ + 6³) | |
| 3 |
| = | (1 + 216) | |
| 3 |
| = |  | × 217 |  | cu.cm. | |
| 3 |
Internal radius of hollow sphere = r cm (let)
| = | π((r + 1)³ + r³) | |
| 3 |
| = | × 217 | |
| 3 |
⇒ r³+ 3r² + 3r + 1 – r³ = 217
⇒ 3r² + 3r + 1 = 217
⇒ 3r² + 3r – 216 = 0
⇒ r² + r – 72 = 0
⇒ r² + 9r – 8r – 72 = 0
⇒ r (r + 9) – 8 (r + 9) = 0
⇒ (r – 8) (r + 9) = 0
⇒ r = 8 cm. because r ≠ –9
∴ External radius of hollow sphere = 9 cm
