The area of the sector of a circle of radius is 32πcm². Find the length of the corresponding arc of the sector.

Correct option is A

Area of a sector:
Area = (π × R² × θ) / 360
32π = (π × (12)² × θ) / 360
32 × 360 = (144 × θ)
θ = (32 × 360) / 144
θ = 80 degrees
Therefore, the angle θ is 80 degrees.
Length of an arc:
Length = (2 × π × R × θ) / 360
Length = (2 × π × 12 × 80) / 360
Length = (16/3) × π cm
Therefore, the length of the arc is (16/3) × π cm.