IGCSE Maths Mensuration (Area & Volume) Notes
Mensuration is measuring shapes — area and perimeter in 2D, volume and surface area in 3D. Choosing the right formula and units is key.
Key concepts
- Area & perimeter
- Area is space inside a shape; perimeter is the distance around it.
- Volume of a prism
- Cross-sectional area × length works for any prism, including cylinders.
- Surface area
- Add the areas of every face or curved surface of a solid.
Key formulas
Circle area
A = πr²
Cylinder volume
V = πr²h
Sphere volume
V = (4/3)πr³
Worked example
Find the volume of a cylinder with radius 3 cm and height 10 cm (to 3 s.f.).
- 1Volume = πr²h.
- 2Substitute: π × 3² × 10 = 90π.
- 3Evaluate: 90 × 3.1416 ≈ 282.7.
Answer: 283 cm³ (3 s.f.)
Common mistakes
✗ Mixing area and volume units.
✓ Area is in cm², volume in cm³ — check the power on the units.
✗ Using diameter instead of radius.
✓ Halve the diameter to get r before using πr².
✗ Rounding too early.
✓ Keep π in the calculator until the final answer.
Quick check
Try these, then reveal the answers.
Area of a circle radius 5 (leave in π)?Reveal answer
25π
Volume of a cube side 4?Reveal answer
64
Units for surface area?Reveal answer
cm² (squared)
Exam tips
- Write the formula before substituting numbers.
- Leave answers in terms of π when the question allows it.
- State units and round to the accuracy requested.
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Frequently asked questions
How do I find the volume of a prism?+
Multiply the area of the cross-section by the length (or height) of the prism.
What is the difference between area and surface area?+
Area applies to flat 2D shapes; surface area is the total area of all faces of a 3D solid.
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