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The radii of two solid iron spheres are 1 cm and 6 cm respectively. A hollow sphere is made by melting the two spheres. If the external radius of the hollow sphere is 9 cm, then its thickness (in cm) is
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- 2
- 1.5
- 0.5
- 1
- 2
Correct Option: D
| Volume of sphere = | πr³ | |
| 3 |
| ∴ Total volume of both spheres = | π(r1³ + r2³) | |
| 3 |
| = | π(1³ + 6³) | |
| 3 |
| = | π(1 + 216) | |
| 3 |
| = |  | × 217 |  | cu.metre. | |
| 3 |
If the internal radius of hollow sphere = r cm, then
| ∴ Volume of the iron of this sphere = | π (9³ - r³) cu.cm. | |
| 3 |
According to the question,
| π (9³ - r³) = | × 217 | |||
| 3 | 3 |
⇒ 729 – r³ = 217
⇒ r³ = 729 – 217 = 512
⇒ r³ = (8)³
⇒ r = 8 cm
∴ Required thickness = 9 – r = 9 – 8 = 1 cm.
