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 set of formulas they only half-remember.
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 subtopics in the Mensuration unit of Cambridge IGCSE Mathematics (0580/0607). Examiners expect you to calculate volume and surface area of standard 3D solids, combine shapes, and convert between units. This guide explains exactly what Solid Geometry covers, how to handle the question types that actually appear, and where to practise each skill.

Key takeaways

• Volume measures space inside a 3D shape (cm³, m³); surface area is the total area of all outer faces (cm², m²).
• Prisms and cylinders use cross-sectional area × length; pyramids and cones use ⅓ × base area × height.
• A sphere has volume ⁴⁄₃πr³ and surface area 4πr² — know which formula the syllabus expects you to use.
• Draw a net or label r, h and slant height clearly before substituting.

What is Solid Geometry in Cambridge IGCSE Maths?

Solid Geometry deals with 3D shapes: cuboids, prisms, cylinders, pyramids, cones and spheres. You calculate volume (how much space they occupy) and surface area (the material needed to cover them). In Cambridge IGCSE Mathematics, questions may give composite solids, ask for capacity in litres, or require you to find a missing dimension when volume is known.

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 / cylinder	Volume = cross-section area × height	”Find the volume of the triangular prism”
Pyramid / cone	Volume = ⅓ × base area × perpendicular height	”A cone has radius 6 cm and height 10 cm”
Surface area	Sum of areas of all faces	”Calculate the total surface area of the cuboid”
Composite solids	Add volumes or subtract a hollow part	”A solid is made from a cylinder and a hemisphere”

How to solve Solid Geometry questions — step by step

The safest method works for every 3D question in this subtopic.

1. Name the solid — prism, cylinder, pyramid, cone or sphere. Sketch it and label r, h and any slant height.
2. Choose volume or surface area from the question wording.
3. Write the formula before substituting — examiners award method marks for this.
4. Calculate each face area for surface area, or the base area first for volume.
5. Convert units if needed (1 litre = 1000 cm³; 1 m³ = 1 000 000 cm³).
6. Check: volume units are cubic; surface area units are square.

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 approach does the question want?

Students lose marks by using the wrong formula or mixing linear and square units. Use the diagram and wording to decide.

Situation	What to do	Typical signal words
Space inside	Volume formula	”volume”, “capacity”, “litres”, “how much water”
Material to cover	Add face areas	”surface area”, “paint”, “wrap”, “label”
Hemisphere on a cylinder	Add or subtract volumes carefully	”attached”, “hollow”, “removed”
Missing dimension	Rearrange volume formula	”The volume is 500 cm³. Find the height.”

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

Most lost marks come from wrong formulas or using diameter instead of radius. 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	Full method with formula	”Work out the volume of the sphere.”
Show that	Prove a given result	”Show that the surface area is 150π cm².”
Give your answer in litres	Convert cm³ to litres	”Give your answer in litres correct to 2 d.p.”
Curved surface area only	Exclude top and bottom faces	”Find the curved surface area of the cylinder.”
Form an equation	Use volume to build algebra	”Form an equation in r and solve.”

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 3 cm. Work out its volume and total surface area.” Volume = 8 × 5 × 3 = 120 cm³. Surface area = 2(40 + 24 + 15) = 158 cm². Mark-scheme reward: both formulas stated with correct units.
2. “A cone has radius 3 cm and perpendicular height 4 cm. Show that its volume is 12π cm³.” Volume = ⅓ × π × 3² × 4 = ⅓ × π × 9 × 4 = 12π cm³. Reward: ⅓ factor and πr²h structure shown on “Show that”.
3. “A cylindrical tank of radius 50 cm is filled to a depth of 80 cm. Work out the volume of water in litres.” Volume = π × 50² × 80 = 200 000π cm³ ≈ 628 319 cm³ → ÷ 1000 ≈ 628 litres (3 s.f.). Reward: litre conversion at the end.

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

Volume builds on Areas and Perimeters — every prism cross-section is a 2D area. Cylinders and cones use Circles for πr² bases. Composite 3D problems often need Pythagoras Theorem to find a perpendicular height. 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

• Using diameter instead of radius in πr² and ⁴⁄₃πr³.
• Forgetting the ⅓ factor for pyramids and cones.
• Calculating total surface area when only the curved surface is asked for.
• Mixing cm³ and litres without dividing by 1000.
• Rounding π too early and losing accuracy marks.

When you need more support

If composite 3D questions keep tripping you up, 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 fixed — difficulty comes from composite shapes, unit conversion and confusing volume with surface area.

Do I need to memorise the sphere formulas? Yes. Volume = ⁴⁄₃πr³ and surface area = 4πr² appear regularly on Extended papers.

What is the difference between height and slant height? Perpendicular height goes straight down from the apex; slant height runs along the sloping face. Use perpendicular height in volume unless the question specifies otherwise.

How do I revise Solid Geometry effectively? Read the subtopic notes, label every diagram with r and h, then take the Solid Geometry quiz. Revisit any composite-solid problems you got wrong before moving on.

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