We use direct proportionality:
360⁰......Pi×R² (full circle)
120⁰.......x
x=120×pi×R²/360=pi×R²/3
x=pi×4²/3=16.76mi²
A=3×pi cm², for an angle of 2×pi/3=120⁰
In a similar way we compute the area of the full circle:
360.........x
120..........3×pi
x=3×pi×360/120=9×pi=3²×pi.
Thus the radius is 3cm.