JAMB 1992 · UME · Q30

The diagram shows a circle with centre $O$ and radius 6 cm; two radii are at right angles. Find the area of the shaded segment.

Worked solution (try it first)

The sector is a quarter circle: $\frac14 \times \pi \times 6^2 = 9\pi\text{ cm}^2$ .
The right-angled triangle on the two radii has area $\frac12 \times 6 \times 6 = 18\text{ cm}^2$ .
Segment = sector − triangle: $9\pi - 18 = 9(\pi - 2)\text{ cm}^2$ , option B.