A chord of a circle subtends an angle of 120^\circ degrees at the centre of a circle of diameter 4\sqrt3 cm. Calculate the area of the major sector.
A
4π cm2
B
32 π cm2
C
16 π cm2
D
8 π cm2
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
Diameter = 4\(\sqrt{3}\) cm
radius = 2\(\sqrt{3}\) cm
Area of major sector = \(\frac{\theta}{360} \times \pi r^{2}\)
\(\theta = 360 - 120 = 240^\circ\)
= \(\frac{240}{360} \times \pi \times 12\)
= \(8\pi cm^{2}\)
Source: Myschool Past Questions Archive (Record #3374)