1. **Problem (a):** A rectangular park measures 50m by 40m. A 3m flower bed is made around the two longer sides and one short side. A circular fish pond of diameter 8.0m is constructed in the centre of the park. Find the area of the grass, correct to the nearest square metre. 2. **Step 1: Calculate the total area of the park.** The area of a rectangle is given by the formula: $$\text{Area} = \text{length} \times \text{width}$$ So, $$\text{Area}_{\text{park}} = 50 \times 40 = 2000 \text{ m}^2$$ 3. **Step 2: Calculate the area covered by the flower bed.** The flower bed is 3m wide around two longer sides (50m sides) and one short side (40m side). - The flower bed extends 3m along the length on both longer sides, so the length including flower beds on both sides is: $$50 + 3 + 3 = 56 \text{ m}$$ - The flower bed extends 3m on one short side only, so the width including flower bed is: $$40 + 3 = 43 \text{ m}$$ 4. **Step 3: Calculate the area including the flower bed on the specified sides.** $$\text{Area}_{\text{with flower bed}} = 56 \times 43 = 2408 \text{ m}^2$$ 5. **Step 4: Calculate the area of the flower bed alone.** $$\text{Area}_{\text{flower bed}} = \text{Area}_{\text{with flower bed}} - \text{Area}_{\text{park}} = 2408 - 2000 = 408 \text{ m}^2$$ 6. **Step 5: Calculate the area of the circular fish pond.** The diameter is 8.0m, so the radius is: $$r = \frac{8.0}{2} = 4.0 \text{ m}$$ The area of a circle is: $$\text{Area} = \pi r^2$$ So, $$\text{Area}_{\text{pond}} = \pi \times 4.0^2 = 16\pi \approx 50.27 \text{ m}^2$$ 7. **Step 6: Calculate the area to be grassed.** The grass area is the original park area minus the pond area and the flower bed area: $$\text{Area}_{\text{grass}} = \text{Area}_{\text{park}} - \text{Area}_{\text{pond}} - \text{Area}_{\text{flower bed}} = 2000 - 50.27 - 408 = 1541.73 \text{ m}^2$$ Rounded to the nearest square metre: $$\boxed{1542 \text{ m}^2}$$ --- 8. **Problem (b):** Find the area of the sector of a circle with radius 35mm and angle 75º, correct to the nearest square millimetre. 9. **Step 1: Recall the formula for the area of a sector.** $$\text{Area}_{\text{sector}} = \frac{\theta}{360} \times \pi r^2$$ where $\theta$ is the central angle in degrees. 10. **Step 2: Substitute the values.** $$r = 35 \text{ mm}, \quad \theta = 75^\circ$$ 11. **Step 3: Calculate the area.** $$\text{Area}_{\text{sector}} = \frac{75}{360} \times \pi \times 35^2 = \frac{75}{360} \times \pi \times 1225$$ 12. **Step 4: Simplify and calculate numerically.** $$\text{Area}_{\text{sector}} = \frac{75}{360} \times 3.1416 \times 1225 \approx 0.2083 \times 3.1416 \times 1225 \approx 800.11 \text{ mm}^2$$ 13. **Step 5: Round to the nearest square millimetre.** $$\boxed{800 \text{ mm}^2}$$