Measurement: Perimeter, Area, Volume and Error
What you must understand
Measurement questions require selecting the correct formula and working consistently in one unit system. Know perimeter and area of rectangles, triangles, circles and composite shapes; volume and surface area of prisms, cylinders, pyramids and spheres; and the relationships between units of length, area and volume. You must also handle Pythagoras' theorem in two and three dimensions, trigonometry in right-angled triangles (sin, cos, tan), and calculations involving speed, distance and time. Accuracy of measurement is examined through absolute error, percentage error and significant figures.
Traps to watch
- Unit conversion for area and volume: 1 m = 100 cm, but 1 m² = 10 000 cm² and 1 m³ = 1 000 000 cm³. Squaring or cubing the conversion factor is the most common error.
- Composite shapes: add areas for joined shapes, but subtract for holes or cut-outs.
- Capacity: 1 cm³ = 1 mL and 1000 cm³ = 1 L; check whether the question asks for volume or capacity.
- Trigonometry: check the calculator is in degree mode, and identify the correct ratio from the given side and the required side.
- Percentage error: divide the error by the measured value, then multiply by 100.
Worked example
A cylindrical tank has radius 1.5 m and height 2 m. Volume = πr²h = π(1.5)²(2) ≈ 14.14 m³. In litres: 14.14 × 1000 = 14 137 L (to the nearest litre).
Rule of thumb
Write the formula, substitute with units, then convert at the end. Sketch the shape and label known lengths before calculating.