Solution:

Provided,

Radius of the circle = 15 cm

θ = 60°

So,

The area of sector OAPB = (60°/360°)×πr² cm²

= 225/6 πcm²

Now, ΔAOB is equilateral because two sides are circle radii and hence equal, and one angle is 60°.

Alternatively, the area of ΔAOB = (√3/4) ×a²

Or, (√3/4) ×15²

Therefore, the area of ΔAOB = 97.31 cm²

Now, Area of OAPB – Area of ΔAOB = Area of minor segment APB

Alternatively, the area of minor segment APB = ((225/6)π – 97.31) cm² = 20.43 cm²

Area of circle – Area of segment APB = Area of major segment

Alternatively, the area of major segment = (π×15²) – 20.4 = 686.06 cm²