Volume measures how much space a solid takes up, and capacity measures how much a container can hold. The same quantity appears in both: a block of 1000 cm³ holds 1 litre.
This module sits after area, perimeter and surface area, because every volume method starts from an area you already know how to find. Check the current 0580 syllabus on the Cambridge page for exactly which solids and formulae your paper expects, and whether a formula list is printed in the exam.
What should I know before starting?
You need to find the area of rectangles, triangles, trapeziums and circles. You also need to substitute into a formula, rearrange a simple formula, and round to 3 significant figures.
If circle area still feels shaky, revisit that first. Every cylinder and cone question depends on it.
An orienting example
A water trough is a prism. Its cross-section is a rectangle 40 cm wide and 25 cm deep, and the trough is 150 cm long. How many litres does it hold when full?
Step 1, cross-section area: 40 × 25 = 1000 cm².
Step 2, volume: 1000 × 150 = 150 000 cm³.
Step 3, capacity: 150 000 ÷ 1000 = 150 litres.
Three ideas appear in one short question: area first, then length, then a unit change. The lessons below take each idea on its own.
In what order should I study the lessons?
- Calculate a prism volume from a cross-section: the core idea, volume = cross-section area × length, which everything else copies.
- Work with a cylinder and a cone: the cylinder is a prism with a circular end, and the cone is one third of it.
- Convert between volume units and capacity: the step where most unit marks are lost.
- Solve a reverse-dimension volume problem: the volume is given and a length is missing.
- Estimate whether a container result is plausible: a quick check that catches slips before you hand in the paper.
Then try the volume and capacity practice set, which mixes all five skills. The non-calculator working trainer helps with the exact arithmetic inside these questions.
What are the common traps?
- Using the slant side as the height. The height in an area or volume formula is always perpendicular.
- Mixing units. A length in metres with another in centimetres gives a volume in neither.
- Squaring the wrong thing. In πr²h the radius is squared, not the whole product.
- Using the diameter as the radius. Read the question for “diameter” and halve it.
- Forgetting the one third in a cone.
- Rounding early. Keep full calculator values until the last line.
How should I use the practice set?
Work through the questions in order, with a calculator unless a question says otherwise. Write each unit on every line. Only then open the worked answer and compare method, not only the final number.
The “if you got these wrong” section at the end of the set points each type of error back to one lesson. Keep a note of which skill the error belonged to, and revisit it a few days later with a fresh question.
If volume errors keep repeating even after this route, online one-to-one Mathematics tuition gives a teacher the chance to see the reasoning behind the mistake while you work.