Volume of a cone formula: V = ⅓πr²h
The volume of a cone formula is V = ⅓πr²h.
What each letter means
- \(V\) the volume
- \(r\) the radius of the base
- \(h\) the perpendicular height (not the slant height)
When to use it
For any cone or conical container. A cone holds one third of the cylinder with the same base and height.
Worked example
A cone has base radius 6 cm and slant height 10 cm. Find its volume, to 3 significant figures.
- \(h=\sqrt{10^2-6^2}=8\)
- \(V=\tfrac13\pi(6)^2(8)=96\pi\)
Answer: \(V=302\text{ cm}^3\)
Common mistake
Using the slant height l instead of the perpendicular height h. If you only know l, use h = √(l² − r²).
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 cone formula?
The volume of a cone formula is V = ⅓πr²h. V: the volume; r: the radius of the base; h: the perpendicular height (not the slant height).
Is the volume of a cone 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 curved surface area of a cone?
Curved surface area = πrl, where l is the slant height, l = √(r² + h²). Add πr² for the base if the cone is solid.
Our own wording, examples and card, checked by IGCSE Math Revision. Not produced or endorsed by Pearson Edexcel.