Paint quantity, coverage risk and tin sizes
A classroom is 8.4 m long, 6.2 m wide and 2.7 m high, and all four walls are to be repainted in one colour. One long wall contains three windows, each 1.5 m by 1.2 m, and one short wall contains a door 0.9 m by 2.1 m. Windows and the door are not painted; neither are the ceiling or floor. The chosen paint covers 16 m² per litre, and the manufacturer advises two coats. Paint is sold in 4 L tins at $62.50 or 10 L tins at $140.00. The business manager wants the cheapest option that still delivers two full coats at the stated coverage.
1. Calculate the paintable wall area and the area to be covered across two coats.
Read the worked answer
Wall area
- Perimeter: 2 × (8.4 + 6.2) = 29.2 m
- Walls: 29.2 × 2.7 = 78.84 m²
Deductions (not painted)
- Windows: 3 × (1.5 × 1.2) = 3 × 1.8 = 5.40 m²
- Door: 0.9 × 2.1 = 1.89 m²
- Total deductions: 7.29 m²
Paintable area: 78.84 − 7.29 = 71.55 m² Two coats: 71.55 × 2 = 143.10 m²
2. Determine how many litres are needed and which purchase option is cheaper.
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- Litres required: 143.10 ÷ 16 = 8.94375 → you cannot buy a fraction of a litre, so 9 L
Option A - 4 L tins: 9 ÷ 4 = 2.25 → 3 tins = 12 L; cost = 3 × $62.50 = $187.50 Option B - 10 L tins: one 10 L tin covers 9 L; cost = $140.00
Option B is cheaper by $187.50 − $140.00 = $47.50, and it carries more paint (10 L vs 9 L needed). Buy the 10 L tin.
3. The painter warns that on this textured wall the real coverage may be up to 15% below the label figure. Reassess the 10 L decision.
Read the worked answer
Recompute litres at reduced coverage:
- 10% loss: 16 × 0.9 = 14.4 m²/L → 143.10 ÷ 14.4 = 9.94 L → a 10 L tin still just covers it (margin 0.06 L).
- 15% loss: 16 × 0.85 = 13.6 m²/L → 143.10 ÷ 13.6 = 10.52 L → the 10 L tin is now short by about 0.5 L, which matters because running out mid-wall means a visible colour or batch mismatch.
Judgement: buy the 10 L tin plus one 4 L tin ($140.00 + $62.50 = $202.50). That still beats three 4 L tins ($187.50)? No - $202.50 is $15.00 more, but it guarantees two full coats with 3.5 L spare for touch-ups. If cost is hard-capped, buy three 4 L tins instead (12 L, $187.50), which also covers the 10.52 L worst case and is the cheaper guaranteed option.