The number of solid spheres ,each of diameter 3 cm that could be mould

1.	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. 162. 243. 364. 48
Answer» 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.

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. 162. 243. 364. 48

Answer» 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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