The diagram shows Jane's lawn - OCR - GCSE Maths - Question 10 - 2020 - Paper 1

To find the area of the three semi-circles:

1. The radius of each semi-circle is half of the square's side: r = rac{36}{2} = 18 ext{ m}

2. The area of one semi-circle is given by: ext{Area of one semi-circle} = rac{1}{2} imes ext{π} r^2 = rac{1}{2} imes ext{π} imes 18^2 Therefore, $ext{Area of one semi-circle} ≈ 508.94 ext{ m}^2$

3. Since there are three semi-circles: $ext{Total area of all semi-circles} ≈ 3 imes 508.94 ≈ 1526.82 ext{ m}^2$

The total area of the lawn is the sum of the area of the square and the area of the semi-circles:

$$ext{Total Area} = 1296 + 1526.82 ≈ 2822.82 ext{ m}^2$$

To find the total amount of fertiliser required:

1. The fertiliser rate is 30g per square metre. Therefore, the total amount needed in grams is:

   $$ext{Total fertiliser (g)} = ext{Total Area} imes ext{Rate} = 2822.82 imes 30 ≈ 84684.6 ext{ g}$$

2. Converting to kilograms:

   ext{Total fertiliser (kg)} = rac{84684.6}{1000} ≈ 84.68 ext{ kg}

Since fertiliser is sold in 10kg bags, the number of bags required is:

ext{Number of bags} = rac{84.68}{10} ≈ 8.468

Thus, rounding up, she needs 9 bags.

The total cost of buying the bags of fertiliser is:

$$ext{Total Cost} = ext{Number of bags} imes ext{Cost per bag} = 9 imes 15.80 = 142.2 ext{ pounds}$$