From arc AB=4πcm, central angle ∠ AOB = 120.
Through the arc length formula
L=nπr/ 180
Know 120πr/ 180=4π.
That is 2πr/3=4π.
That is 2r/3=4.
That is, r=6
Therefore, the area of sector AOB is
S=nπr^2/360
= 120π*6^2/360
=π*6^2/3
= 12π