JAMB 2002 · UME · Q12

A chord of a circle subtends an angle of $120^\circ$ at the centre of a circle of diameter $4\sqrt3$ cm. Calculate the area of the major sector.

Worked solution (try it first)

The radius is half of $4\sqrt3$ , so $r = 2\sqrt3$ cm and $r^2 = 12$ .
The major sector has angle $360^\circ - 120^\circ = 240^\circ$ , which is $\frac23$ of the circle.
Area $= \frac23 \times 12\pi = 8\pi\text{ cm}^2$ , option C.