Knowledge organisers

Mensuration: Cambridge IGCSE Maths (0580) knowledge organiser

Everything to know about mensuration on one page: key definitions, the formulas, a worked example, the mistakes to avoid and a checklist of what you should be able to do.

Download the A4 sheet (PDF)

Key definitions

Perimeter: The total distance around the outside of a shape.
Area: The amount of flat space a shape covers, in square units.
Volume: The amount of space a solid takes up, in cubic units.
Sector: The part of a circle between two radii and an arc.

Key formulas

Formulas marked with a label are given in the exam (we only say so where our formula sheet confirms it). Learn the rest.

TriangleOn the 0580 formula list	\(A=\tfrac12bh\)
Parallelogram; trapezium	\(A=bh;\) \(A=\tfrac12(a+b)h\)
CircleOn the 0580 formula list	\(A=\pi r^2,\) \(C=2\pi r\)
Arc; sector (angle \(\theta\))	\(\text{arc}=\frac{\theta}{360}\times2\pi r,\) \(\text{sector}=\frac{\theta}{360}\times\pi r^2\)
Curved surface: cylinder; cone (slant \(l\))On the 0580 formula list	\(A=2\pi rh;\) \(A=\pi rl\)
Sphere, surface areaOn the 0580 formula list	\(A=4\pi r^2\)
Prism; pyramidOn the 0580 formula list	\(V=Al;\) \(V=\tfrac13Ah\)
Cylinder; coneOn the 0580 formula list	\(V=\pi r^2h;\) \(V=\tfrac13\pi r^2h\)
Sphere, volumeOn the 0580 formula list	\(V=\tfrac43\pi r^3\)

Worked example

A cylinder has radius 3 cm and height 10 cm. Find its volume, leaving your answer in terms of π.

V = πr²h
V = π × 9 × 10

Answer: 90π cm³ (about 283 cm³)

Common mistakes

Mixing units in area and volume
Map scales: not converting centimetres to kilometres
Area of a trapezium: the formula is not on the formula list

More on what examiners see students get wrong: Examiner Insights.

You should be able to…

Convert between metric units of length, area, volume and capacity, such as m² to cm² and cm³ to litres.
Calculate the circumference and area of a circle, giving answers to a set accuracy or in terms of π, and find a radius from an area.
Calculate the surface area and volume of cuboids, prisms and cylinders, including problems such as filling a container.
Find perimeters and areas of compound shapes and parts of shapes, such as a segment or a shape with a semicircle removed.
Find arc lengths and areas of major and minor sectors, and work backwards to find the angle or the radius from a given arc or area.
Practise giving exact answers without a calculator, using exact trigonometric values and leaving answers in terms of π.

The printable sheet

Mensuration knowledge organiser for Cambridge IGCSE Maths (0580): one A4 page of key definitions, formulas, a worked example and common mistakes — Mensuration knowledge organiser (Cambridge IGCSE Maths (0580)), A4. Download the PDF.

Revise it next

Other Cambridge IGCSE Maths (0580) topics: Number · Algebra and graphs · Coordinate geometry · Geometry · Trigonometry · Transformations and vectors · Probability · Statistics · All Cambridge IGCSE Maths (0580) organisers