Classroom Painting Cost and Coverage
A school in Yaoundé plans to repaint one classroom. The room is 9 m long, 7 m wide and 3.2 m high. The four walls and the ceiling are to receive two coats of paint; the floor is not painted. There are two doors, each 2 m by 1 m, three windows, each 1.5 m by 1.2 m, and one blackboard 4 m by 1.2 m. Doors, windows and the blackboard are not painted. One litre of paint covers 10 m² per coat. Paint is sold in 5-litre tins at 18,000 XAF each and in 1-litre tins at 4,500 XAF each. The school has budgeted 120,000 XAF for paint and wants to avoid buying more tins than necessary. The bursar also asks whether using one coat instead of two would be an acceptable saving, given that the paint manufacturer recommends two coats for a washable finish.
1. Calculate the total paintable area in square metres. Show the wall, ceiling and deduction calculations.
Read the worked answer
Wall area = 2(9 + 7) × 3.2 = 2 × 16 × 3.2 = 102.4 m². Ceiling area = 9 × 7 = 63 m². Gross area = 102.4 + 63 = 165.4 m². Deductions: doors = 2 × 2 × 1 = 4 m²; windows = 3 × 1.5 × 1.2 = 3 × 1.8 = 5.4 m²; blackboard = 4 × 1.2 = 4.8 m². Total deductions = 4 + 5.4 + 4.8 = 14.2 m². Paintable area = 165.4 − 14.2 = 151.2 m².
2. For two coats, find the litres of paint needed and the cheapest way to buy it. State whether the 120,000 XAF budget is enough.
Read the worked answer
Two-coat area = 151.2 × 2 = 302.4 m². Paint needed = 302.4 ÷ 10 = 30.24 L, so 31 L must be bought because paint is sold in whole litres. Cheapest combination: 6 five-litre tins give 30 L and cost 6 × 18,000 = 108,000 XAF; one 1-litre tin costs 4,500 XAF. Total = 31 L for 112,500 XAF. Check alternatives: 7 five-litre tins = 35 L for 126,000 XAF; 31 one-litre tins = 139,500 XAF; 5 five-litre tins plus 6 one-litre tins = 31 L for 90,000 + 27,000 = 117,000 XAF. So 6 five-litre tins plus 1 one-litre tin is cheapest. 112,500 XAF is within the 120,000 XAF budget, leaving 7,500 XAF.
3. Compare the cost of one coat with two coats and advise the bursar whether to use one coat. Consider the manufacturer's recommendation.
Read the worked answer
One-coat area = 151.2 m². Paint needed = 151.2 ÷ 10 = 15.12 L, so 16 L must be bought. Cheapest purchase: 3 five-litre tins (15 L) at 3 × 18,000 = 54,000 XAF plus 1 one-litre tin at 4,500 XAF = 58,500 XAF. Four five-litre tins cost 72,000 XAF, and 16 one-litre tins cost 72,000 XAF. Saving from one coat = 112,500 − 58,500 = 54,000 XAF. However, the manufacturer recommends two coats for a washable finish. One coat may leave a thin, uneven finish that is hard to clean and may need repainting sooner; the saving could be lost in extra labour and paint later. If the classroom must be washable and durable, use two coats. If the wall is in good condition and only a temporary refresh is needed, one coat could be accepted, but the bursar should record that it is a compromise.