Volume of a sphere formula: V = ⁴⁄₃πr³
The volume of a sphere formula is V = ⁴⁄₃πr³ (surface area A = 4πr²).
What each letter means
- \(V\) the volume
- \(A\) the surface area
- \(r\) the radius
When to use it
For balls, bubbles, planets and hemispheres (half of each formula, plus the flat face πr² for the surface of a solid hemisphere).
Worked example
Find the volume of a solid hemisphere of radius 5 cm, to 3 significant figures.
- Half a sphere: \(V=\tfrac12\times\tfrac43\pi(5)^3=\tfrac{250}{3}\pi\)
Answer: \(V=262\text{ cm}^3\)
Common mistake
Using the diameter as r. Halve the diameter first.
On your course
| Course | In the exam |
|---|---|
| Edexcel 4MA1 (Higher) | On the formulae page of the Higher papers |
| Cambridge 0580 | On the list of formulas printed in the paper |
From our own IGCSE Maths formula sheets, in our words. Official: Pearson's 4MA1 specification (PDF, Appendix 5) · Cambridge's 0580 syllabus (PDF).
Practise and revise
Questions
What is the volume of a sphere formula?
The volume of a sphere formula is V = ⁴⁄₃πr³ (surface area A = 4πr²). V: the volume; A: the surface area; r: the radius.
Is the volume of a sphere given in the exam?
Edexcel 4MA1 (Higher): on the formulae page of the Higher papers. Cambridge 0580: on the list of formulas printed in the paper. This comes from our own IGCSE Maths formula sheets; your teacher has the official booklet.
What is the surface area of a sphere?
Surface area = 4πr². A hemisphere has curved surface 2πr², plus πr² for the flat face if it is solid.
Our own wording, examples and card, checked by IGCSE Math Revision. Not produced or endorsed by Pearson Edexcel.