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A right circular cylinder is partially filled with water. Two iron spherical balls are completely immersed in the water so that the height of the water in the cylinder rises by 4 cm. If the radius of one ball is half of the other and the diameter of the cylinder is 18 cm., then the radii of the spherical balls are
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- 6 cm. and 12 cm.
- 4 cm. and 8 cm.
- 3 cm. and 6 cm.
- 2 cm. and 4 cm.
- 6 cm. and 12 cm.
Correct Option: C
Volume of both spheres = Volume of water raised in the cylinder
= π × 9² × 4 = 324π cu. cm.
Radius of first sphere = r cm.
| Radius of second sphere = | cm | |
| 2 |
| ∴ | π |  | r³ + |  | = 324π | ||
| 3 | 8 |
| ⇒ | | | = | ||
| 8 | 4 |
| ⇒ | = 243 | |
| 8 |
| ⇒ r³ = | = 216 | |
| 9 |
| ∴ r = | = 6 cm. | |
| 3 |
∴ Radius of second sphere = 3 cm.
