Measurement: Perimeter, Area, Volume and Accuracy
What you must understand
Measurement questions require you to choose the correct formula, apply it with consistent units, and round sensibly. You need perimeter and area of rectangles, triangles, circles and composite shapes; volume of prisms and cylinders; surface area of simple solids; and Pythagoras' theorem for right-angled triangles. You also need to convert between units of length, area and volume, and to work with significant figures, decimal places and percentage error.
Traps that appear in questions
- Area and volume unit conversions. 1 m = 100 cm, but 1 m² = 10 000 cm² and 1 m³ = 1 000 000 cm³. Multiplying by 100 for area or volume is a very common error.
- Composite shapes. Add areas of parts, but do not double-count shared edges; for perimeter, count only the outside boundary.
- Degrees versus radians on the calculator. Keep the calculator in degree mode for angle work.
- Pythagoras and the hypotenuse. The hypotenuse is always the side opposite the right angle and is the longest side; identify it before squaring.
- Rounding too early. Carry full calculator values through the working and round only at the end.
- Percentage error. Use error ÷ true value × 100%, and take the magnitude, not a negative value.
Worked example
A cylindrical tank has radius 1.2 m and height 2.5 m. Volume = πr²h = π × 1.44 × 2.5 ≈ 11.31 m³. Converting to litres, multiply by 1000: about 11 310 L. If the tank is filled to 80%, the water volume is 0.8 × 11.31 ≈ 9.05 m³, about 9050 L.
Rule of thumb
Write the formula, substitute with units shown, compute, then round to a sensible number of significant figures and check that the size of the answer is plausible.