# 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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## Options:

1. 6 cm and 12 cm

2. 4 cm and 8 cm

3. 3 cm and 6 cm

4. 2 cm and 4 cm

### Correct Answer: Option 3 (Solution Below)

This question was previously asked in

SSC CGL Tier-II Quant Previous Paper 18 (Held On: 30 November 2016)

SSC CGL Tier 2 Quant Previous Paper 14 (Held On: 30 November 2016)

## Solution:

Let the radii of the spherical balls be r cm and r/2 cm.

Radius of the cylinder R = 18/2 = 9 cm.

According to the question

(4/3) π [r3 + (r/2)3] = π R2 h

⇒ (4/3) [r3 + r3/8] = 9 × 9 × 4

⇒ 9r3/8 = 9 × 9 × 3

⇒ r3 = 9 × 3 × 8

⇒ r = ∛[3 × 3 × 3 × 2 × 2 × 2]

⇒ r = 3 × 2

⇒ r = 6 cm

⇒ r/2 = 3 cm

So, radii of the cylinder are 3 cm and 6 cm.
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