16 An area to be landscaped is a sector with a radius of 19 metres and an angle at the centre of 145^(@). The area is to be covered with turf at $12.50 per square metre and then top-dressed with soil at $2.30 per square metre. Find the total cost of the landscaping to the nearest dollar.

Question

16 An area to be landscaped is a sector with a radius of 19 metres and an angle at the centre of  145^(@). The area is to be covered with turf at  $12.50 per square metre and then top-dressed with soil at  $2.30 per square metre. Find the total cost of the landscaping to the nearest dollar.

Bytelearn · Accepted Answer

Calculate Area of Sector: To find the total cost of landscaping, we first need to calculate the area of the sector. The formula for the area of a sector is (θ/360) * π * r^2, where θ is the angle in degrees and r is the radius. Area of the sector = (145/360) * π * (19)^2Perform Calculation: Now we perform the calculation using the values provided. Area of the sector = (145/360) * π * 361 Area of the sector ≈ (0.4027777778) * π * 361 Area of the sector ≈ 453.7777778 square metres (rounded to the nearest tenth)Cost of Turf: Next, we calculate the cost of covering the area with turf at $12.50 per square metre. Cost of turf = Area of the sector * Cost per square metre of turf Cost of turf ≈ 453.7777778 * 12.50 Cost of turf ≈ $5672.2222225Cost of Soil: We also need to calculate the cost of top-dressing the area with soil at $2.30 per square metre. Cost of soil = Area of the sector * Cost per square metre of soil Cost of soil ≈ 453.7777778 * 2.30 Cost of soil ≈ $1043.68888934Find Total Cost: Finally, we add the cost of turf and the cost of soil to find the total cost of landscaping. Total cost = Cost of turf + Cost of soil Total cost ≈ $5672.2222225 + $1043.68888934 Total cost ≈ $6715.91111184Round Total Cost: We round the total cost to the nearest dollar as requested. Total cost ≈ $6716

Full solution

More problems from Weighted averages: word problems

Related topics