A few lead spheres of diameter 6 cm are dropped into a cylindrical beaker containing some water such that they are fully submerged. If the diameter of the beaker is 9 cm and the water level has risen by 32 cm, find the number of lead spheres dropped into the beaker.

Question

Question

This question was previously asked in

NTPC CBT-I (Held On: 4 Jan 2021 Shift 2)

Answer 1

Given:

The radius of the sphere is 3 cm

Radius & height of cylinder are 4.5 cm & 32cm

Formula used:

The volume of sphere = 4/3πr³

The volume of cylinder = πr²h

Calculations:

The volume of sphere inserted = volume of water risen

Radius of sphere = 6/2= 3 cm

Radius of cylinder = 9/2 = 4.5

So,

(4/3)π × (3)³ × Number of sphere = π (4.5) × (4.5) × 32

⇒ Number of sphere = 18

∴ The correct choice is option 2.

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