10.6.5 Making a Garden

Notepad iconActivity: 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 one times m super two 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.

Solutions icon

Answer

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:

length multiplication width equals eight m prefix multiplication of five m equation left hand side equals right hand side 40 times m super two

The diameter of the pond is 2 m, so its radius is 1 m. The area is calculated as follows:

the area of a circle multirelation equals pi multiplication open radius close squared equals pi multiplication one times m super two almost equals 3.14 times m super two

The radius of the patio is five m division two equals two .5 m. The area of a circle of radius 2.5 m = equation left hand side pi multiplication 2.5 times m super two almost equals right hand side 19.63 times m super two.

The semicircular patio is half this area:

Area of patio = equation left hand side 19.63 times m super two division two almost equals right hand side 9.82 times m super two.

The flower beds are each quarter of a circle of radius 1 m. The area of a circle of radius 1 m = equation left hand side pi multiplication one squared times m super two equals right hand side 3.14 times m super two. So two quarter circles total area = equation left hand side two multiplication pi division four times m super two almost equals right hand side 1.57 times m super two.

The lawn area is equal to the area of the garden, minus the area of the pond, the patio, and the beds.

The lawn area equals area of garden minus area of pond minus area of patio minus areas of beds

So, lawn area, in meters squared, = 40 minus 3.14 minus 9.82 minus 1.57 equals 25.47.

Because you cannot purchase part of a roll, this answer means that 26 times m super two 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.

10.6.4 Calculator Exploration: Areas of Circles

10.6.6 Converting Between Area Units