Paving the Community Garden
A community garden has a rectangular lawn measuring 8.4 m by 6.2 m. A circular pond of radius 1.5 m sits in the middle of the lawn and will be kept, with a paved edge around it. Every other part of the lawn is to be covered with square concrete pavers measuring 40 cm by 40 cm.
The pavers are sold only in packs of 12. The landscape supplier recommends ordering 10% extra area to allow for cuts and breakages. Edging strip for the outside boundary of the lawn is sold in 2.4 m lengths and is not needed around the pond. Pavers cost $34.50 per pack and edging costs $18.90 per length. Use π ≈ 3.14.
1. Calculate the number of paver packs that must be ordered.
Read the worked answer
Lawn area: 8.4 × 6.2 = 52.08 m² Pond area: π r² = 3.14 × 1.5² = 3.14 × 2.25 = 7.065 m² Area to pave: 52.08 − 7.065 = 45.015 m² Add 10% waste: 45.015 × 1.10 = 49.5165 m²
Coverage per pack: each paver is 0.4 × 0.4 = 0.16 m², so a pack of 12 covers 12 × 0.16 = 1.92 m².
Packs: 49.5165 ÷ 1.92 = 25.79… → round up to 26 packs.
Check: 25 packs cover 48.00 m², which is less than the 49.52 m² required; 26 packs cover 49.92 m², which is enough. The answer must round up because half a pack cannot be bought.
2. Work out the total cost of pavers and edging.
Read the worked answer
Pavers: 26 × $34.50 = $897.00
Edging: the strip runs around the outside of the rectangular lawn only. Perimeter = 2 × (8.4 + 6.2) = 2 × 14.6 = 29.2 m Lengths needed = 29.2 ÷ 2.4 = 12.17… → 13 lengths 13 × $18.90 = $245.70
Total: $897.00 + $245.70 = $1142.70
Both parts had to be rounded up: 12 lengths would give 28.8 m and leave a 0.4 m gap on the boundary, which cannot be joined invisibly.
3. A committee member argues: 'Buy 25 packs instead - the offcuts from the pond curve will cover the difference.' Assess this argument.
Read the worked answer
What 25 packs give: 25 × 1.92 = 48.00 m² What is needed including allowance: 49.52 m² Shortfall: 49.52 − 48.00 = 1.52 m², about 1.52 ÷ 0.16 ≈ 10 pavers.
Without any waste allowance the job needs 45.015 m², which is 45.015 ÷ 1.92 = 23.4 → 24 packs. So the dispute is entirely about whether the 10% allowance is realistic.
Judgement: the pond is circular, so the pavers along its edge must be cut on a curve and almost every one of those cuts wastes the offcut. Offcuts from a curved cut are small triangles that cannot be reused elsewhere. A 10% allowance is therefore reasonable, and 25 packs is short by roughly 10 pavers plus any breakages. Buying 26 packs is the sound decision: an extra pack costs $34.50, while a second delivery for a few missing pavers would cost more and delay the job.