Oyo Water Tank: Capacity, Paint and a Rival Cuboid
A community development association in Oyo is buying an overhead water tank. The chosen tank is a closed cylinder of radius 1.4 m and height 3 m. It will stand on a concrete platform 1.2 m high, and the top of the tank must stay below a roof beam whose underside is 4.5 m above the ground. A paint contractor charges ₦2,500 per litre of paint supplied and applied; one litre covers 8 m² per coat, and the association wants two coats on the whole outer surface of the tank, including the flat top and the base, which is painted before the tank is lifted. A rival supplier offers a cuboid tank measuring 2 m by 2 m by 3 m at the same price. The water committee estimates that each of 6 households will draw 120 litres per day, and the tank is refilled once a week. Take π = 3.142 and give answers to a sensible degree of accuracy.
1. Calculate the capacity of the cylindrical tank in litres and decide whether a single weekly fill is enough for the 6 households.
Read the worked answer
Volume. V = πr²h = 3.142 × (1.4)² × 3 = 3.142 × 1.96 × 3 = 3.142 × 5.88 = 18.47496 ≈ 18.475 m³.
Convert. 1 m³ = 1,000 litres, so capacity ≈ 18,475 litres.
Demand. Six households × 120 litres × 7 days = 5,040 litres per week.
Comparison. 5,040 ÷ 18,475 ≈ 0.273, so the weekly draw is about 27% of one fill. A single fill would last 18,475 ÷ (6 × 120) ≈ 25.7 days.
Judgement. One refill a week is comfortably sufficient; at that rate the tank is never below about 73% full, which also leaves a reserve for firefighting or guests. The danger in this question is mixing square and cubic units - using 1.96 × 3 without the π factor, or converting m³ to litres by multiplying by 100 instead of 1,000.
2. Find the quantity of paint that must be bought for two coats on the whole outer surface, and the cost.
Read the worked answer
Surface of a closed cylinder. Two circular ends plus the curved surface: A = 2πr² + 2πrh = 2πr(r + h) = 2 × 3.142 × 1.4 × (1.4 + 3)
Step by step:
- 2 × 3.142 = 6.284
- 6.284 × 1.4 = 8.7976
- 8.7976 × 4.4 = 38.70944 ≈ 38.71 m²
Two coats. 38.71 × 2 = 77.42 m² of coverage needed.
Litres. 77.42 ÷ 8 = 9.68 litres.
Buying rule. Paint is supplied in whole litres and a partly used litre cannot be returned, so 9 litres (72 m²) would leave 5.42 m² uncoated. Buy 10 litres.
Cost. 10 × ₦2,500 = ₦25,000.
Judgement. Quoting ₦24,194 (the exact 9.68 litres) is not a real quotation; the correct answer must round up, and the cost is taken on the rounded quantity.
3. Compare the cylindrical tank with the cuboid alternative and check the height clearance under the roof beam. What would you advise the association?
Read the worked answer
Cuboid capacity. V = 2 × 2 × 3 = 12 m³ = 12,000 litres. The cylinder holds 18,475 − 12,000 = 6,475 litres more, i.e. 18,475 ÷ 12,000 ≈ 1.54 times as much - about 54% extra for the same price.
Height clearance. Platform 1.2 m + cylinder height 3 m = 4.2 m. The beam underside is at 4.5 m, leaving 4.5 − 4.2 = 0.3 m of clearance. The tank fits, but only just: any additional plinth, lagging or a raised lid would break the limit, so the installation drawing should record the 0.3 m margin. (The cuboid, also 3 m tall, gives the same 4.2 m.)
Footprint check. The cylinder's diameter is 2 × 1.4 = 2.8 m, so the platform must be at least 2.8 m across - wider than the 2 m square needed for the cuboid, which is the one practical advantage of the rival tank.
Advice. Buy the cylinder: it stores about 6,475 litres more for the same price, fits under the beam, and the extra water gives a wider safety margin against supply interruptions. The only condition is that the concrete platform be built at least 2.8 m wide and designed for the greater mass of water (about 18.5 tonnes when full).