Painting and Skirting a Recruit Classroom
A recruit classroom is a rectangular room 12.5 m long, 7.2 m wide and 2.8 m high. It has two external doors, each 2.0 m high and 0.9 m wide, and three windows, each 1.5 m wide and 1.2 m high. The walls are to receive two coats of emulsion. One litre of paint covers 11 m² per coat, and paint is supplied in 5-litre tins costing £38.50 each. The flooring contractor will lay vinyl at £14.25 per square metre over the whole floor. New skirting board is to run around the room except across the two door openings; it comes in 2.4 m lengths at £7.80 each. The works officer wants a materials estimate that includes a 10% allowance on paint for cutting in and uneven surfaces, but no allowance on skirting because offcuts can be used at corners. You must decide the number of paint tins, the vinyl cost and the number of skirting lengths.
1. Calculate the paintable wall area after deducting doors and windows.
Read the worked answer
Perimeter = 2 × (12.5 + 7.2) = 2 × 19.7 = 39.4 m. Gross wall area = 39.4 × 2.8 = 110.32 m². Doors: 2 × (2.0 × 0.9) = 2 × 1.8 = 3.6 m². Windows: 3 × (1.5 × 1.2) = 3 × 1.8 = 5.4 m². Total deductions = 9.0 m². Paintable area = 110.32 − 9.0 = 101.32 m². If a ceiling were included it would add 12.5 × 7.2 = 90 m², but the question specifies walls only; including it would nearly double the paint order.
2. Calculate the number of 5-litre tins required for two coats with the 10% allowance, and the paint cost.
Read the worked answer
Two-coat area = 101.32 × 2 = 202.64 m². Add 10%: 202.64 × 1.10 = 222.904 m². Paint needed = 222.904 ÷ 11 = 20.264 L. Tins are 5 L, so 20.264 ÷ 5 = 4.05 → 5 tins. Four tins give 20 L, which is 0.264 L short, so rounding down would fail. Cost = 5 × £38.50 = £192.50. Without the 10% allowance, 202.64 ÷ 11 = 18.42 L → 4 tins (20 L), so the allowance changes the order by one tin and £38.50.
3. Calculate the vinyl cost and the number of 2.4 m skirting lengths required, including the effect of the door openings.
Read the worked answer
Floor area = 12.5 × 7.2 = 90.0 m². Vinyl cost = 90.0 × £14.25 = £1,282.50. Skirting run = perimeter − two door widths = 39.4 − (2 × 0.9) = 39.4 − 1.8 = 37.6 m. Lengths = 37.6 ÷ 2.4 = 15.67 → 16 lengths. Sixteen lengths give 38.4 m, leaving 0.8 m of offcut; fifteen lengths give only 36.0 m, 1.6 m short. Cost = 16 × £7.80 = £124.80. No 10% allowance is added, as instructed, because the 0.8 m offcut and corner cuts can be absorbed within the 16 lengths.