Water tank, paint and concrete slab
A school buys a cylindrical water tank for its vegetable garden. The tank has a diameter of 1.4 m and a height of 2.0 m, and it stands on a square concrete slab measuring 2.4 m by 2.4 m by 0.12 m thick. Gardeners fill their watering cans from the tank using 20-litre buckets. Before the rainy season the outside of the tank must be painted with two coats; the curved surface and the flat top are painted, but the base rests on the slab and is not painted. One litre of paint covers 8 m², paint is sold only in 1-litre tins costing P68.50 each, and concrete is ordered in multiples of 0.25 m³ at P1 950 per m³. Use π = 22/7.
1. Calculate the capacity of the tank in litres, and state how many full 20-litre buckets can be filled from a full tank.
Read the worked answer
Diameter 1.4 m, so radius r = 0.7 m and height h = 2.0 m.
Volume = πr²h = (22/7) × 0.7² × 2.0
0.7² = 0.49, and (22/7) × 0.49 = 22 × 0.07 = 1.54
Volume = 1.54 × 2.0 = 3.08 m³
1 m³ = 1 000 litres, so capacity = 3.08 × 1 000 = 3 080 litres.
Buckets: 3 080 ÷ 20 = 154 buckets.
The division is exact, so a full tank fills 154 buckets completely with nothing left over. (If the tank were only partly filled, the answer would have to be rounded down to the nearest whole bucket.)
2. How many tins of paint must be bought, and what will the paint cost? Explain which surfaces you included and which you left out.
Read the worked answer
Curved surface: 2πrh = 2 × (22/7) × 0.7 × 2.0 = 8.8 m²
Top circle: πr² = (22/7) × 0.49 = 1.54 m²
Base: not painted, because it stands on the slab and no one can see or reach it.
Area for one coat = 8.8 + 1.54 = 10.34 m²
Two coats: 2 × 10.34 = 20.68 m²
Paint needed: 20.68 ÷ 8 = 2.585 litres.
Paint is sold only in whole 1-litre tins, so round up to 3 tins - buying 2 tins (16 m²) would leave part of the second coat unfinished.
Cost: 3 × P68.50 = P205.50.
The rounding up matters: 0.585 of a litre looks small, but paint cannot be bought in fractions of a tin, and left-over paint is not waste because it can be used for touching up rust spots.
3. Calculate the volume of the concrete slab and the cost of the concrete, taking account of the way concrete must be ordered.
Read the worked answer
Volume of slab = length × breadth × thickness
= 2.4 × 2.4 × 0.12
2.4 × 2.4 = 5.76, and 5.76 × 0.12 = 0.6912 m³
Concrete is ordered in multiples of 0.25 m³: 0.25, 0.50, 0.75, 1.00 …
0.6912 lies between 0.50 and 0.75, so 0.50 m³ would be too little and the order must be 0.75 m³.
Cost = 0.75 × P1 950 = P1 462.50
Unused concrete = 0.75 − 0.6912 = 0.0588 m³, about 59 litres, worth 0.0588 × P1 950 ≈ P114.66. Rounding the volume to 0.7 m³ and multiplying would give the wrong answer, because 0.7 m³ is not a quantity the supplier will deliver.