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By melting a solid lead sphere of diameter 12 cm, three small spheres are made whose diameters are in the ratio 3 : 4 : 5. The radius (in cm) of the smallest sphere is
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- 3
- 6
- 1.5
- 4
- 3
Correct Option: A
| Volume of original sphere = | π(6)³ = 128π cm³ | |
| 3 |
Let the radii of small spheres be 3x, 4x and 5x cm respectively
| ∴ | π[(3x)³ + (4x)³ + (5x)³] = 288 π | |
| 3 |
| ⇒ | π[27x³ + 64x³ + 125³] = 288 π | |
| 3 |
| ⇒ | π× 216x³ = 288 π | |
| 3 |
| ⇒ x³ = | = 1 | |
| 4π × 216 |
⇒ x = 1
∴ Required radius = 3 × 1 = 3cm.
