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 4 cm and height 9 cm. Find its volume.
- \(V=\tfrac13\pi(4)^2(9)=48\pi\)
Answer: \(V=151\text{ cm}^3\) (3 s.f.)
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 |
|---|---|
| AA SL | In the IB formula booklet |
| AI SL | In the IB formula booklet |
| AA HL | In the IB formula booklet |
| AI HL | In the IB formula booklet |
From our own IB Maths formula sheets, in our words. The IB gives its booklet to schools, so we checked against our own copy: your teacher has the official one. Official: IB DP Mathematics page.
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?
AA SL: in the IB formula booklet. AI SL: in the IB formula booklet. AA HL: in the IB formula booklet. AI HL: in the IB formula booklet. This comes from our own IB 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 IB Math Revision. Not produced or endorsed by the International Baccalaureate Organization.