IGCSE Math RevisionCambridge IGCSE Maths (0580) · Revision notes · Topic 5 of 9
Cambridge IGCSE Maths 0580 Mensuration Notes
Revision notes for topic 5, Mensuration, of the Cambridge IGCSE Mathematics (0580) syllabus for exams from 2025 to 2030 (Cambridge says the 2028–2030 syllabus has no significant changes that affect teaching). Each of the 5 sub-topics lists what the syllabus asks, marked Core or Extended, with a short explanation and a worked example. Cover the answer and try each example first.
- 5 sub-topics
- 5 Core and Extended
- 0 Extended only
Core Core students (Papers 1 and 3) learn the Core statements. Extended Extended students (Papers 2 and 4) learn everything: the Core statements, the Extended additions and the Extended-only sub-topics. Papers 1 and 2 are non-calculator.
5.1 Units of measure
Core C5.1 Extended E5.1
- Metric units of mass, length, area, volume and capacity; convert between larger and smaller units
Same mathematics as Edexcel 4MA1.
Revise it
From our Edexcel 4MA1 Higher notes, so it may go beyond Core: Core students need only the Core statements above.
When converting units of area, square the linear factor (1 m² = 100² cm²). For volume, cube it.
Example: Convert 3 m² to cm².
Answer: 3 × 100² = 30 000 cm².
0580 practice questions
8 questions written for 0580 in the Mensuration practice: 8 Core, 4 non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:
Practice question (Core, non-calculator, 2 marks):
Convert
(a) 3.5 km to metres (b) 750 g to kilograms.
Show the answer and mark scheme
- B1 (a) 3500 m
- B1 (b) 0.75 kg
Answer: (a)
Practice question (Core, calculator, 3 marks):
A tank in the shape of a cuboid measures 1.2 m by 80 cm by 50 cm.
How many litres of water does it hold when full?
Show the answer and mark scheme
- M1 converts to the same unit, e.g. 120 cm
- M1 120 × 80 × 50 = 480 000 cm³
- A1 480 litres
Answer:
0580 questions: Units of Measure questions (Core and Extended, with worked answers)
Edexcel 4MA1 notes: Area & Volume Conversions
Practise (4MA1 questions, same mathematics): Units and Compound Measures questions
5.2 Area and perimeter
Core C5.2 Extended E5.2
- Perimeter and area of rectangles, triangles, parallelograms and trapezia
Same mathematics as Edexcel 4MA1.
Revise it
From our Edexcel 4MA1 Higher notes, so it may go beyond Core: Core students need only the Core statements above.
Composite areas break a shape into rectangles + triangles + circles then sum.
Example: Area of a trapezium with parallel sides 12 & 18 cm, height 8 cm.
Answer: = ½(12 + 18) × 8 = 120 cm².
0580 practice questions
8 questions written for 0580 in the Mensuration practice: 8 Core, 5 non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:
Practice question (Core, non-calculator, 2 marks):
A rectangle is 7 cm long and 4.5 cm wide. Find
(a) its perimeter (b) its area.
Show the answer and mark scheme
- B1 (a) 23 cm
- B1 (b) 31.5 cm²
Answer: (a)
Practice question (Core, non-calculator, 3 marks):
A trapezium has parallel sides of length
Find
Show the answer and mark scheme
- M1 ½ × (x + x + 6) × 8 = 104
- M1 8x + 24 = 104
- A1 x = 10
Answer:
0580 questions: Area and Perimeter questions (Core and Extended, with worked answers)
Edexcel 4MA1 notes: 2D Perimeter & Area
Practise (4MA1 questions, same mathematics): Area and Perimeter questions
5.3 Circles, arcs and sectors
Core C5.3 Extended E5.3
- Circumference and area of a circle
- Arc length and sector area as fractions of the circle, where the sector angle is a factor of 360°
Extended also: Arc length and sector area for any angle, including major and minor sectors, and finding the angle or radius from them.
Same mathematics as Edexcel 4MA1.
0580 practice questions
8 questions written for 0580 in the Mensuration practice: 7 Core and 1 Extended, 3 non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:
Practice question (Core, non-calculator, 2 marks):
A circle has radius 5 cm. Find, in terms of
(a) its circumference (b) its area.
Show the answer and mark scheme
- B1 (a) 10π cm
- B1 (b) 25π cm²
Answer: (a)
Practice question (Extended, calculator, 4 marks):
A sector of a circle has radius 9 cm and arc length 12 cm.
(a) Work out the angle of the sector. Give your answer correct to 1 decimal place.
(b) Work out the area of the sector.
Show the answer and mark scheme
- M1 (a) θ/360 × 2 × π × 9 = 12
- A1 76.4°
- M1 (b) 76.39…/360 × π × 9², or ½ × 9 × 12
- A1 54 cm²
Answer: (a)
0580 questions: Circles, Arcs and Sectors questions (Core and Extended, with worked answers)
Edexcel 4MA1 notes: 2D Perimeter & Area
Practise (4MA1 questions, same mathematics): Circles, Arcs and Sectors questions
5.4 Surface area and volume
Core C5.4 Extended E5.4
- Surface area and volume of cuboids, prisms, cylinders, spheres, pyramids and cones
Same mathematics as Edexcel 4MA1.
Revise it
From our Edexcel 4MA1 Higher notes, so it may go beyond Core: Core students need only the Core statements above.
Volume of a prism = cross-section area × length. Cylinders use πr² for the area.
Example: Triangular prism, cross-section area 24 cm², length 15 cm. Volume?
Answer: = 24 × 15 = 360 cm³.
0580 practice questions
8 questions written for 0580 in the Mensuration practice: 8 Core, 3 non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:
Practice question (Core, non-calculator, 2 marks):
A cuboid measures 6 cm by 2 cm by 5 cm. Find
(a) its volume (b) its total surface area.
Show the answer and mark scheme
- B1 (a) 60 cm³
- B1 (b) 104 cm²
Answer: (a)
Practice question (Core, calculator, 3 marks):
A cone has radius 5 cm and volume 314 cm³.
[The volume of a cone is
Work out the height of the cone. Give your answer correct to 3 significant figures.
Show the answer and mark scheme
- M1 ⅓ × π × 5² × h = 314
- M1 h = 3 × 314 ÷ (25π)
- A1 12.0 cm (11.99…)
Answer:
0580 questions: Surface Area and Volume questions (Core and Extended, with worked answers)
Edexcel 4MA1 notes: Volume of Prisms · Surface Area of Prisms
Practise (4MA1 questions, same mathematics): Volume and Surface Area questions
5.5 Compound shapes and parts of shapes
Core C5.5 Extended E5.5
- Perimeter and area of compound shapes and parts of shapes
- Surface area and volume of compound solids and parts of solids
Extended also: Harder parts of solids, such as frustums and hemispheres.
Same mathematics as Edexcel 4MA1.
0580 practice questions
15 questions written for 0580 in the Mensuration practice: 12 Core and 3 Extended, 5 non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:
Practice question (Core, non-calculator, 2 marks):
A shape is made from a rectangle 9 cm long and 5 cm wide, with a right-angled triangle on one of its 5 cm sides. The triangle has base 5 cm and height 4 cm.
Work out the area of the shape.
Show the answer and mark scheme
- M1 9 × 5 + ½ × 5 × 4
- A1 55 cm²
Answer:
Practice question (Core, calculator, 3 marks):
A running track has two straight sides, each 85 m long, and two semicircular ends, each with diameter 64 m.
Work out the perimeter of the track. Give your answer correct to the nearest metre.
Show the answer and mark scheme
- M1 two semicircles make one circle: π × 64
- M1 2 × 85 + 64π
- A1 371 m
Answer:
0580 questions: Compound Shapes questions (Core and Extended, with worked answers)
Edexcel 4MA1 notes: 2D Perimeter & Area · Volume of Prisms
Practise (4MA1 questions, same mathematics): Area and Perimeter questions · Circles, Arcs and Sectors questions · Volume and Surface Area questions
Practise mensuration
47 practice questions are written for 0580 on every sub-topic of this topic. For the 5 sub-topics that are the same mathematics in Edexcel 4MA1, the practice also has our 4MA1 Higher questions, which are Extended level. Core students: use the Core filter on the practice page; every sub-topic with Core content has questions written for 0580 Core. Practice is part of the IGCSE plan, with a free preview; these notes are free.
- Mensuration practice for 0580: the 47 questions written for 0580, tagged Core or Extended and non-calculator or calculator, with the Edexcel 4MA1 Higher questions for the sub-topics that are the same mathematics
- Student hub: the Edexcel 4MA1 units (Unit 1, Unit 5), each question marked
- Cambridge IGCSE Maths 0580 past papers: the 2025 specimen papers and past papers, with a timer
- Formulas for mensuration on the one-page 0580 formula sheet (free PDF), showing which are on the paper's formula list
- Cambridge 0580 mensuration questions by topic, Core and Extended, with worked answers
- Knowledge organiser: Mensuration on one page (printable)
Try it now
1 of 5
- Question 1 of 5
- Question 2 of 5
- Question 3 of 5
- Question 4 of 5
- Question 5 of 5
5 quick questions on area and perimeter. No sign-in needed.
Knowledge organiser: Mensuration on one page (key facts, formulas and mistakes to avoid; printable PDF)
Questions about mensuration
What is in Cambridge IGCSE 0580 mensuration?
Topic 5 has 5 sub-topics: 5.1 Units of measure; 5.2 Area and perimeter; 5.3 Circles, arcs and sectors; 5.4 Surface area and volume; 5.5 Compound shapes and parts of shapes.
Which mensuration sub-topics are Extended only?
None: every sub-topic has Core content. Extended students (Papers 2 and 4) also learn the Extended statements marked in each sub-topic.
What do students get wrong in mensuration?
Mixing units in area and volume; Area of a trapezium: the formula is not on the formula list. Our 0580 Examiner Insights page explains each one with a fix.
Are these notes free?
Yes. Every note and worked example on these pages is free to read, with no sign-in.