JAMB - Mathematics (2002 - No. 24)

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

4π cm²

32 π cm²

16 π cm²

8 π cm²

Diameter = 4\(\sqrt{3}\) cm

radius = 2\(\sqrt{3}\) cm

Area of major sector = \(\frac{\theta}{360} \times \pi r^{2}\)

\(\theta = 360 - 120 = 240°\)

= \(\frac{240}{360} \times \pi \times 12\)

= \(8\pi cm^{2}\)