The volume and surface area formulas
litres = πr²h × 1,000 (with r and h in metres)
A = 2πr² + 2πrh
Where the formula comes from
The volume is the cylinder formula, πr²h. Working in metres gives cubic metres, and since a cubic metre is exactly 1,000 litres — because a litre is a cubic decimetre and there are 1,000 of those in a cubic metre — the conversion is a single multiplication.
A worked example, step by step
A tank 0.5 m in radius and 2 m tall
- Base area: π × 0.5² = 0.785 m².
- Volume: 0.785 × 2 = 1.571 m³.
- Capacity: 1.571 × 1,000 = 1,571 litres.
- Sheet metal: 2π × 0.5² + 2π × 0.5 × 2 = 7.85 m².
Watch the units: volume goes in cubic units and surface area in square ones. Mixing them is the most common mistake.
Where it turns up in practice
Water tanks, fuel storage, brewing vessels and rainwater harvesting. The sheet metal figure matters for costing, since material is usually priced by the square metre and the ends are a surprisingly large share on short, wide tanks.