Physical quantities & measurement

Measuring length and volume

Measuring length and volume Core 3 min read

Instruments and units

In physics, every measurement must include a number and a unit. The International System of Units (SI) is used throughout Cambridge IGCSE Physics.

Length is the SI base quantity for distance. Its SI unit is the metre (m). Common multiples and sub-multiples:

Unit	Symbol	Relation to metre
kilometre	km	1 km = 1000 m
centimetre	cm	100 cm = 1 m
millimetre	mm	1000 mm = 1 m

Using a ruler

A metre rule (or shorter 30 cm rule) is used to measure length directly.

Correct procedure

Place the zero mark of the rule exactly at one end of the object.
Read the scale at the other end of the object.
Keep your eye directly above the mark (not to the side).

Parallax error — Reading the ruler with your eye to one side makes the reading appear shifted. Always view the scale with your line of sight perpendicular to the ruler. In a diagram question, the correct reading is the one where the line of sight is at 90° to the scale.

Ruler scale (side view) ⬆ Eye directly above the graduation mark

Vernier callipers and micrometers

For smaller lengths, more precise instruments are used.

Instrument	Range	Precision	Use
Ruler	0–1 m	±1 mm	General lengths
Vernier callipers	0–150 mm	±0.1 mm	External/internal widths, depths
Micrometer screw gauge	0–25 mm	±0.01 mm	Wire diameter, paper thickness

At IGCSE level you are expected to describe how to use a ruler correctly and explain parallax error. Reading Vernier callipers or a micrometer may appear in Paper 6 (Alternative to Practical) — but the principle of eye position applies to all.

Measuring volume

Volume is the amount of three-dimensional space occupied by an object. SI unit: cubic metre (m³). For liquids, the cubic centimetre (cm³) or millilitre (mL) is used (1 cm³ = 1 mL).

Regular shapes

For objects with a regular shape, volume is calculated from length measurements:

Cube: \( V = l^3 \)
Cuboid: \( V = l \times w \times h \)
Cylinder: \( V = \pi r^2 h \)
Sphere: \( V = \tfrac{4}{3}\pi r^3 \)

Measuring cylinder

A measuring cylinder (graduated cylinder) is used to measure the volume of a liquid directly. It has a scale marked in cm³.

Correct reading procedure

Place the cylinder on a flat, level surface.
Lower your eye to the level of the liquid surface.
Read the bottom of the meniscus (the curved surface of the water).

Read at the bottom of the curve (meniscus)

For water and most liquids, the meniscus curves downward — read the bottom. For mercury, the meniscus curves upward — read the top (not examinable at IGCSE but good to know).

Volume by displacement

An irregular solid that does not dissolve in water can be measured using the displacement method.

Displacement method

Part-fill a measuring cylinder with water. Record the initial volume \( V_1 \).
Carefully lower the solid into the water using a thread.
Record the new volume \( V_2 \).
Volume of solid = \( V_2 - V_1 \)

Worked example — volume by displacement

A stone is lowered into a measuring cylinder containing 30 cm³ of water. The water level rises to 42 cm³. Calculate the volume of the stone.

Solution:

\( V_{\text{stone}} = V_2 - V_1 = 42 - 30 = 12 \text{ cm}^3 \)

Notice: the answer has the same unit as the scale on the measuring cylinder (cm³).

Exam mark schemes often award one mark for each correct procedural step. For the displacement method: state the initial and final readings and the subtraction. Three steps = potentially three marks.