area of a cirlce=πr²
a circle has 360º
Therefore:
πr²/360º=area of a sector/degrees of this sector
area of a sector=(πr²)(degrees of this sector / 360º
Data:
r=14.6 mm
degrees of this sector=300º
area of a sector=π(14.6 mm)²(300º) / 360º=177.6333...π mm²≈117.63π mm².
if π≈3.1416 then :
Area of a sector=177.63 (3.1416) mm²=558.05 mm²
Answer: the area of this sector is 177.63π mm² or 558.05 mm².