10.6.5 Making a Garden
Activity: Making a Garden
The sketch shows a rough plan of a garden, which contains a circular pond, a semicircular patio, and two flower beds with circular front edges.
The remaining part of the garden is to be covered in lawn sod. If sod is sold in rolls, how many rolls will be needed? If you get stuck, try the strategies we used for the insulation problem in Unit 4 such as “I know/I want” and taking small steps.
We want to work out how many rolls of sod are needed, and that means estimating the area of the lawn in square meters. Working to two decimal places throughout the calculation will provide sufficient precision. The patio, pond, and flower beds will not be covered with sod, so we need to subtract these areas from the total area of the garden.
The garden is a rectangle, so the area can be calculated as follows:
The diameter of the pond is 2 m, so its radius is 1 m. The area is calculated as follows:
The radius of the patio is . The area of a circle of radius 2.5 m = .
The semicircular patio is half this area:
Area of patio = .
The flower beds are each quarter of a circle of radius 1 m. The area of a circle of radius 1 m = . So two quarter circles total area = .
The lawn area is equal to the area of the garden, minus the area of the pond, the patio, and the beds.
So, lawn area, in meters squared, = .
Because you cannot purchase part of a roll, this answer means that of sod, or 26 rolls, will be needed to cover the entire area. Note that if you wished to calculate the area of the lawn more precisely, you would need to use full calculator accuracy in the calculations. However, this estimate is sufficient for this situation.