11+ Volume and Capacity: Cuboids, Cubes and Worked Questions

A box can have a large base and still hold very little if it is shallow. Volume measures space in three dimensions, so a useful calculation needs height as well as length and width. Before multiplying, decide whether the question describes the outside of a solid or the space available inside a container.

These original explanations and questions support preparation for 11-plus exams taken in 2027. They are not official papers or a complete school syllabus. Check your target school’s guidance and try each question before opening the explanation. Written English models show a supported response, not the only acceptable wording.

Build the formula from layers

Imagine a cuboid made from one-centimetre cubes. A base measuring 7 cm by 4 cm holds 28 cubes in one layer. Five layers hold 28 × 5 = 140 cubes. Each little cube occupies 1 cm³, so the total is 140 cm³. This explains why a cuboid’s volume is length × width × height: the first multiplication counts one layer and the third dimension counts the layers.

Worked example: find a missing dimension

A cuboid has volume 216 cm³ and a base 9 cm by 4 cm. The base area is 36 cm². Divide the volume by that area: height = 216 ÷ 36 = 6 cm. Multiply back to check: 9 × 4 × 6 = 216. An answer in cm² would describe area rather than the missing length.

Connect volume to capacity carefully

One millilitre occupies one cubic centimetre; 1,000 cm³ is one litre. A tank with internal dimensions 25 cm by 16 cm by 20 cm has an ideal brim capacity of 8,000 cm³, or 8 litres. External dimensions do not establish internal capacity when the wall thickness is unknown. In a real container, a safe filling level may also be below the brim.

A volume ratio alone does not prove a packing arrangement

To pack 2 cm cubes in a box whose internal dimensions are 10 cm by 6 cm by 4 cm, align their edges with the box. There are 5 along the length, 3 across and 2 layers: 30 cubes. Each dimension fits exactly here. Dividing volumes can give an upper bound, but for different sizes it does not alone prove that the objects fit without gaps or overlap.

Eight original questions

Explain a mistake by its dimension

If you used only two measurements, you calculated a base area. If you multiplied a mixture of centimetres and metres, convert first and begin again. If all edges doubled but your volume only doubled, write the three new dimensions separately. These checks diagnose the reasoning rather than merely replacing a wrong final number.

Choose a useful next step

Review metric conversions before mixing units, and compare volume with area and perimeter. Return to the maths learning hub or explore original practice and worked answers.

Sources and scope

The DfE programme of study provides a curriculum reference, not a promise about every school’s test. Examples and questions on this page are original; no school affiliation or educator endorsement is implied.