1. **Problem statement:** In a park, circular flower beds with diameter $d = 4.90$ m are created. (a) A flower bed is to be bordered with boxwood plants. There are 5 plants per meter. Calculate the cost. (b) A flower bed is to be planted with roses. There are 8 roses per square meter. Calculate the cost. (c) Around the flower bed, a 1.20 m wide path is laid. 1 m² costs 26 plus 19% VAT. Calculate the cost. --- 2. **Formulas and rules:** - Circumference of a circle: $$C = \pi d$$ - Area of a circle: $$A = \pi r^2$$ where $r = \frac{d}{2}$ - Cost = number of plants × price per plant - For the path, area of larger circle minus area of flower bed - VAT is added as 19% of the base cost --- 3. **Calculations:** **(a) Boxwood plants cost:** - Diameter $d = 4.90$ m, so circumference $$C = \pi \times 4.90 = 15.386$$ m (approx) - Number of plants = $5 \times 15.386 = 76.93 \approx 77$ plants - Price per boxwood plant = 2.85 - Total cost = $77 \times 2.85 = 219.45$ **(b) Rose plants cost:** - Radius $r = \frac{4.90}{2} = 2.45$ m - Area $$A = \pi \times 2.45^2 = \pi \times 6.0025 = 18.85$$ m² (approx) - Number of roses = $8 \times 18.85 = 150.8 \approx 151$ roses - Price per rose plant = 7.25 - Total cost = $151 \times 7.25 = 1094.75$ **(c) Path cost:** - Outer radius = $2.45 + 1.20 = 3.65$ m - Outer area $$A_{outer} = \pi \times 3.65^2 = \pi \times 13.3225 = 41.85$$ m² (approx) - Path area = $41.85 - 18.85 = 23.00$ m² - Cost per m² = 26 - Base cost = $23.00 \times 26 = 598$ - VAT = $0.19 \times 598 = 113.62$ - Total cost = $598 + 113.62 = 711.62$ --- 4. **Final answers:** - (a) Boxwood plants cost: **219.45** - (b) Rose plants cost: **1094.75** - (c) Path cost including VAT: **711.62**