Who this is for: Cambridge IGCSE Mathematics (0580/0607) students who want Solid Geometry — volume and surface area of prisms, cylinders, pyramids, cones and spheres — to become a reliable source of marks instead of a jumble of 3D formulas.
What query it owns: how to understand and revise Solid Geometry in Cambridge IGCSE Mathematics.
Why this is safe: this page owns the Solid Geometry revision-guide angle, while Tutopiya’s Solid Geometry subtopic page owns the learning resource and the free Solid Geometry quiz owns the practice.

Solid Geometry is one of the highest-mark areas in the Mensuration unit of Cambridge IGCSE Mathematics (0580/0607). Whenever a question involves a 3D shape — a cuboid, cylinder, pyramid or sphere — examiners expect you to identify the correct formula, substitute dimensions carefully and give answers with the right units. This guide explains the solids that actually appear, how to tackle volume and surface area, and where to practise each skill.

Key takeaways

• Volume measures the space inside a 3D shape (cm³, m³); surface area is the total area of all outer faces (cm², m²).
• Prism volume = cross-sectional area × length; cylinder volume = πr²h.
• For pyramids and cones, volume = ⅓ × base area × height — do not forget the one-third factor.
• Always state the formula, show substitution and give the final answer with correct units.

What is Solid Geometry in Cambridge IGCSE Maths?

Solid Geometry is the study of three-dimensional shapes: their volume (capacity) and surface area (total outer covering). In Cambridge IGCSE Mathematics it covers prisms, cylinders, pyramids, cones and spheres, often in real-world contexts such as tanks, packaging and construction. Questions may ask for a missing dimension, a comparison of capacities, or the cost of material to cover a surface.

You can read the full explanation, worked examples and notes on Tutopiya’s Solid Geometry subtopic page before you attempt questions.

The core ideas you must master

These four ideas appear again and again. Learn what each one means and the exam phrasing that signals it.

Idea	What it means	How the exam uses it
Prism	Uniform cross-section; V = area of cross-section × length	”Calculate the volume of the triangular prism”
Cylinder	V = πr²h; curved surface = 2πrh	”Work out the volume of the cylinder”
Pyramid / cone	V = ⅓ × base area × height	”Find the volume of the square-based pyramid”
Sphere	V = ⁴⁄₃πr³; surface area = 4πr²	”Calculate the volume of the sphere”

How to find volume and surface area — step by step

The safest method works for every solid in the syllabus.

1. Name the solid — prism, cylinder, pyramid, cone or sphere.
2. Write the correct formula before substituting any numbers.
3. Find the cross-sectional area for prisms; identify radius and height for cylinders.
4. Substitute and calculate; use π on your calculator unless told to use 3.14 or 22/7.
5. For surface area, add the areas of every face — draw a net if it helps.
6. State units: cm³ or m³ for volume; cm² or m² for surface area.

Once you have worked through a few, test yourself with the free Solid Geometry quiz — it tells you fast whether the method has actually stuck.

Volume vs surface area: which does the question want?

Students lose marks by using a volume formula when the question asks for surface area, or by forgetting the ⅓ in pyramid volume. Use the wording to decide.

Situation	What to do	Typical signal words
Space inside a 3D shape	Use a volume formula	”volume”, “capacity”, “litres”, “how much water”
Material to cover the outside	Use surface area	”surface area”, “paint”, “wrap”, “label”
Missing dimension	Rearrange the formula	”The volume is 500 cm³. Work out the height.”
Composite solid	Split into known shapes	”The solid is made from a cylinder and a hemisphere”

Solid Geometry in past-paper wording: command words that matter

Most lost marks come from misreading the command word or using the wrong solid formula. These are the command words you will see and what each one demands.

Command word / phrase	What the question wants	Typical stem
Calculate / Work out	Find volume or surface area with full method	”Work out the volume of the cylinder.”
Show that	Prove a given result — the answer is stated	”Show that the volume of the sphere is 113 cm³.”
Write down	State a value; minimal working (usually 1 mark)	“Write down the volume of the cuboid.”
Give your answer correct to …	Round as instructed	”Give your answer correct to 3 significant figures.”
Convert	Change units (e.g. cm³ to litres)	“Give your answer in litres.”

Worked exam-style stems (how to answer the wording)

Practising the wording — not just the formulas — is what method marks reward. Here is how three real-style stems are answered.

1. “A cuboid is 8 cm by 5 cm by 4 cm. Calculate the volume and the total surface area.” Volume = 8 × 5 × 4 = 160 cm³. Surface area = 2(40 + 32 + 20) = 184 cm². Mark-scheme reward: both formulas stated, correct units on each answer.
2. “A cylinder has radius 3 cm and height 10 cm. Show that its volume is 90π cm³.” V = π × 3² × 10 = 90π. Reward: full substitution shown — writing 90π alone without working scores nothing on “Show that”.
3. “A cone has base radius 6 cm and height 8 cm. Work out the volume.” V = ⅓ × π × 6² × 8 = ⅓ × π × 288 = 96π cm³ (≈ 302 cm³ to 3 s.f.). Reward: the ⅓ factor included in working.

When you can recognise the wording instantly, work the full set on the Mensuration topical past paper questions and the Solid Geometry quiz to lock the method in.

How Solid Geometry connects to the rest of Mensuration

3D skills build on Areas and Perimeters, because every prism volume starts with a 2D cross-sectional area, and on Circles, which supplies the πr² terms in cylinders and spheres. When you are ready to mix topics, the Cambridge IGCSE Maths resource hub lets you move straight from a weak subtopic into the next.

Common mistakes students make

• Forgetting the ⅓ factor for pyramids and cones.
• Using diameter instead of radius in πr² formulas.
• Confusing volume (cubic units) with surface area (square units).
• On surface area, missing a face — especially the top or bottom of an open container.
• Rounding π too early and losing accuracy marks on multi-step questions.

When you need more support

If volume and surface area questions keep tripping you up — especially composite solids — work through the Mensuration topical past paper questions and the Solid Geometry quiz to pinpoint the exact gap, then get focused help from a Cambridge IGCSE Maths tutor to fix it quickly.

Frequently asked questions

Is Solid Geometry hard in Cambridge IGCSE Maths? The formulas are manageable once you know which solid you are dealing with. Marks are lost when students forget ⅓ for pyramids, mix up radius and diameter, or confuse volume with surface area.

What is the quickest way to find the volume of a prism? Find the area of the cross-section, then multiply by the length (or height) of the prism.

How do I find the surface area of a cylinder? Add the curved surface (2πrh) to the two circular ends (2 × πr²): total = 2πrh + 2πr².

How do I revise Solid Geometry effectively? Read the subtopic notes, sketch a net for surface-area questions, then take the Solid Geometry quiz. Revisit any composite-solid problems you got wrong before moving on.

Ready to master Cambridge IGCSE Maths Solid Geometry?

Start with the Solid Geometry subtopic page, then book a free trial with a Cambridge IGCSE Maths specialist to turn Solid Geometry into guaranteed marks.

Ready to Excel in Your Studies?

Get personalised help from Tutopiya's expert tutors. Whether it's IGCSE, IB, A-Levels, or any other curriculum — we match you with the perfect tutor and your first session is free.

Book Your Free Trial