1. **Calculate the area of the sector of a circle with radius 65 mm and sector angle 42°.** - The formula for the area of a sector is $$Area = \frac{\theta}{360} \times \pi r^2$$ where $\theta$ is the sector angle in degrees and $r$ is the radius. - Given: $r = 65$ mm and $\theta = 42^\circ$. - Convert radius into cm: $65$ mm = $6.5$ cm. - Calculate the area: $$Area = \frac{42}{360} \times \pi \times (6.5)^2 = \frac{42}{360} \times \pi \times 42.25$$ $$Area \approx 0.1167 \times 3.1416 \times 42.25 \approx 15.48\ \text{cm}^2$$ 2. **Work out the area of the shaded segment formed by a quarter circle with radius 4.8 cm and chord AC.** - The arc ABC is a quarter circle, so $\theta = 90^\circ$. - Radius $r = 4.8$ cm. - Calculate the area of the sector: $$Area_{sector} = \frac{90}{360} \times \pi \times (4.8)^2 = \frac{1}{4} \times \pi \times 23.04 = 18.1\ \text{cm}^2$$ - Calculate the length of chord AC using the right triangle formed: $$AC = \sqrt{(4.8)^2 + (4.8)^2} = \sqrt{46.08} = 6.788\ \text{cm}$$ - Calculate the area of triangle OAC: $$Area_{triangle} = \frac{1}{2} \times 4.8 \times 4.8 = 11.52\ \text{cm}^2$$ - The shaded segment area = sector area - triangle area: $$Area_{segment} = 18.1 - 11.52 = 6.58\ \text{cm}^2$$ - Rounded to 3 significant figures: $6.58$ cm². **Final answers:** 1. Sector area = $15.48$ cm². 2. Segment area = $6.58$ cm².