What is important to know about Volume of pyramids, cones & spheres?

Volume of a pyramid = ⅓ × base area × height.

What is important to know about Volume of pyramids, cones & spheres?

Volume of a cone = ⅓ × π × r² × h.

What is important to know about Volume of pyramids, cones & spheres?

Volume of a sphere = (4/3) × π × r³.

📏

Geometry & Measures · Higher

Volume of pyramids, cones & spheres

Pyramids, cones and spheres have specific volume formulas. These are given on the formula sheet in some exams, but you need to know how to apply them correctly.

Revising volume of pyramids, cones & spheres the night before an exam? These are condensed revision notes — the facts, formulas and mistakes examiners actually mark, with no long explanations. Prefer a full walkthrough with step-by-step reasoning instead? Search “Volume of pyramids, cones & spheres GCSE” on the site for the complete guide.

🔑

Key facts to remember

1Volume of a pyramid = ⅓ × base area × height.
2Volume of a cone = ⅓ × π × r² × h.
3Volume of a sphere = (4/3) × π × r³.
4Curved surface area of a cone = πrl (where l = slant height).
5Surface area of a sphere = 4πr².
6The height used in the cone formula is the perpendicular height, not the slant height.

📐

Formulas

Pyramid volume

V = ⅓ × base area × h

Cone volume

V = ⅓πr²h

Sphere volume

V = (4/3)πr³

Cone curved surface area

CSA = πrl

l = slant height

Sphere surface area

SA = 4πr²

✍️

Worked examples

Example 1

Find the volume of a cone with radius 5 cm and perpendicular height 9 cm. Give your answer in terms of π.

Working

V = ⅓ × π × r² × h
V = ⅓ × π × 25 × 9
V = ⅓ × 225π = 75π cm³

Answer75π cm³

Example 2

A sphere has a volume of 288π cm³. Find its radius.

Working

(4/3)πr³ = 288π
(4/3)r³ = 288
r³ = 288 × (3/4) = 216
r = ∛216 = 6 cm

Answerr = 6 cm

⚠️

Common mistakes

✗Using the slant height instead of the perpendicular height for cone volume.

✗Forgetting the ⅓ in the pyramid and cone formulas.

✗Squaring instead of cubing r in the sphere volume formula.

🎯

Exam tips

✓These formulas may be given — but know what each letter represents so you can substitute correctly.

✓For spheres and cones: identify r first; for cones also identify h (perpendicular) and l (slant) separately.

Ready to test yourself on Volume of pyramids, cones & spheres?

Get AI-marked practice questions on exactly this subtopic.

Practice this topic →

← All topics Dashboard

▶️ Watch on YouTube

Free video lessons

Click a topic to search

▶volume cone sphere pyramid GCSE Higher ▶sphere volume formula GCSE maths ▶cone volume GCSE Higher ▶pyramid volume GCSE maths

Opens YouTube — pick any free GCSE video.