CH-16-001 · Composite stadium: reverse perimeter and surfacing cost
A recreation area consists of a rectangle with a semicircle attached to each short side. The diameter of each semicircle is 16 m. The perimeter is m. Surface material costs £4 per m². The contractor orders 15% extra material. Work out the total material cost to the nearest penny. Material can be bought in any amount.
Circles & Composite Area with Percentage Multiplier
Booklet p. 38, p. 51 & p. 83
Method
1) Subtract 2πr from perimeter to find straight lengths L
2) Total area = Rectangle (2rL) + Circle (πr²)
3) Multiply by (1 + waste%) and cost per m²
Worked Example (CH-16-001)
1)
The two arcs have total length 16π m.
2)
Two straight lengths total 52 m, so each is 26 m.
3)
Rectangle area = 416 m²; two semicircles form a circle of area 64π m².
4)
Total area = 617.06193… m²; multiply by 1.15 for extra material.
5)
Multiply unrounded order area by £4 per m².
6)
£2838.48
Ans =
£2838.48