Measurement
What you must understand
Measurement covers length, mass, capacity, time, money, temperature, perimeter, area, surface area and volume, together with unit conversion and compound measures such as speed, density and rates. You must know the area formulae for triangles, parallelograms, trapezia and circles, the volume formulae for prisms, cylinders and spheres, and how to work with composite shapes. Accuracy of units matters as much as accuracy of arithmetic.
Traps that appear in questions
- Mixed units. Convert to a single unit before calculating: 1 m² = 10 000 cm², not 100 cm².
- Perimeter versus area. Perimeter is a length; area is measured in square units.
- π and rounding. Use the value stated in the question, or keep π in the working until the final step.
- Speed, distance, time. Rearrange carefully: time = distance ÷ speed, and convert minutes to hours for decimal answers.
- Composite shapes. Add or subtract the simple parts, and do not double-count shared edges.
- Capacity. 1 litre = 1000 cm³; 1 m³ = 1000 litres.
Worked example
A cylindrical tank has radius 0.5 m and height 2 m. Volume = πr²h = π × 0.5² × 2 = 0.5π ≈ 1.571 m³. In litres: 1.571 × 1000 ≈ 1571 litres, to the nearest litre.
Rule of thumb
Write the formula, substitute with units attached, then check the answer's size against common sense - a classroom is not 500 m long, and a cup does not hold 5 litres.