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The number of solid spheres ,each of diameter 3 cm that could be moulded to form a solid metal cylinder of height 54 cm and diameter 4 cm is?
1. 16
2. 24
3. 36
4. 48

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Correct Answer - Option 4 : 48

Given:

Diameter of the each sphere = 3 cm

Diameter of the solid metal cylinder = 4 cm

Height of the solid metal cylinder = 54 cm

Concept used: 

Volume of spherical ball = 4/3 × π × r3

Volume of cylinder = π × r2 × h

Number of small balls (n) = (Volume of cylinder)/(Volume of sphere)

Calculation:

Let the number of solid spheres be n.

Radius of the each sphere = 3/2 cm

Radius of the solid metal cylinder = 4/2 = 2 cm

Volume of each sphere = (4/3) × π × (3/2)3 

⇒  π × (4/3) × (27/8)

⇒ 9π/2 cm3

Volume the solid metal cylinder = π × (2)2 × 54 = 216π cm3

n = 216π/(9π/2)

⇒ n = 48

∴  The number of solid spheres is 48.

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