Area and volume formulas for every shape you're likely to need — triangles, circles, cylinders, cones, spheres — with worked examples and the reasoning behind the formulas.
Whether you're tiling a floor, filling a pool, or just sitting a maths exam, area and volume calculations come up constantly. Here are all the key formulas with worked examples.
Triangle: Base 8m, height 5m → A = ½ × 8 × 5 = 20m²
Circle: Radius 7cm → A = π × 7² = π × 49 ≈ 153.9cm²
Trapezium: Parallel sides 6m and 10m, height 4m → A = ½ × (6 + 10) × 4 = 32m²
Cylinder (swimming pool): Radius 4m, depth 1.5m → V = π × 4² × 1.5 = π × 16 × 1.5 ≈ 75.4m³ = 75,400 litres
Sphere (football): Radius 11cm → V = 4/3 × π × 11³ = 4/3 × π × 1331 ≈ 5,575cm³
Cone: Base radius 3m, height 5m → V = 1/3 × π × 3² × 5 = 1/3 × π × 45 ≈ 47.1m³
How many litres in a cylindrical tank? Calculate volume in m³ then multiply by 1,000 (1m³ = 1,000 litres).
How much soil for a raised garden bed? It's a cuboid — length × width × depth in metres gives volume in m³. Multiply by 1,000 for litres, or divide by 0.025 to get the number of standard 25-litre bags.
Concrete for a circular post hole? Cylinder formula — π × radius² × depth. Most pre-mix bags cover about 0.01m³ each.