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

The radius of each semi-circle is half the side of the square:

ext{radius} = rac{36}{2} = 18 ext{ m}

The area of one full circle is:

$$ext{Area}_{ ext{circle}} = ext{π} imes r^2 = ext{π} imes (18)^2 = 324 ext{π} ext{ m}^2$$

Since we have three semi-circles, the total area is:

ext{Area}_{ ext{semi-circles}} = 3 imes rac{1}{2} imes ext{Area}_{ ext{circle}} = 3 imes rac{1}{2} imes 324 ext{π} = 486 ext{π} ext{ m}^2

To find the total area of the lawn, we add the area of the square and the total area of the semi-circles:

$$ext{Total Area} = ext{Area}_{ ext{square}} + ext{Area}_{ ext{semi-circles}} = 1296 + 486 ext{π} ext{ m}^2$$

Using the approximation for π (3.14):

$ext{Total Area} ext{ (approximated)} = 1296 + 486 imes 3.14 \approx 1296 + 1527.24 \approx 2823.24 ext{ m}^2$

The fertiliser is to be spread at a rate of 30g per square metre. Thus, the total weight of fertiliser needed can be calculated as follows:

$$ext{Total Weight} = ext{Total Area} imes 30 = 2823.24 imes 30 ext{ g} \approx 84697.2 ext{ g} = 84.6972 ext{ kg}$$

Since the fertiliser is sold in 10kg bags, we need to divide the total weight by 10:

$$ext{Number of Bags} = \frac{84.6972}{10} \approx 8.46972$$

Since we cannot buy a fraction of a bag, we round up to 9 bags.

Finally, we calculate the total cost of the fertiliser:

$$ext{Total Cost} = ext{Number of Bags} imes ext{Cost per Bag} = 9 imes 15.80 = 142.2 ext{ £}$$

Thus, the total cost of buying the bags of fertiliser for her lawn is £142.20.