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.