A chord of a circle subtends an angle of 120^\circ at the centre of a circle of diameter \(4\sqrt{3} cm\). Calculate the area of the major sector.
A
32\(\pi\) cm\(^2\)
B
4\(\pi\) cm\(^2\)
C
8\(\pi\) cm\(^2\)
D
16\(\pi\) cm\(^2\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
Angle of major sector = 360^\circ - 120^\circ = 240^\circ
Area of major sector : \(\frac{\theta}{360} \times \pi r^{2}\)
r = \(\frac{4\sqrt{3}}{2} = 2\sqrt{3} cm\)
Area : \(\frac{240}{360} \times \pi \times (2\sqrt{3})^{2}\)
= \(8\pi cm^{2}\)
Source: Myschool Past Questions Archive (Record #54920)