A chord of a circle subtends an angle of 120° at the centre of a circle of diameter 43–√cm 4 3 c m . Calculate the area of the major sector.

A chord of a circle subtends an angle of 120° at the centre of a circle of diameter 43–√cm $4\sqrt{3}cm$. Calculate the area of the major sector.

Answer Details

Angle of major sector = 360° - 120° = 240°

Area of major sector : θ360×πr2 $\frac{\theta }{360}\times \pi r^2$

r = 43√2=23–√cm $\frac{4\sqrt{3}}{2}=2\sqrt{3}cm$

Area : 240360×π×(23–√)2 $\frac{240}{360}\times \pi \times (2\sqrt{3}{)}^2$

= 8πcm2