Volume of a cylinder formula: V = πr²h
The volume of a cylinder formula is V = πr²h (curved surface area = 2πrh).
What each letter means
- \(V\) the volume
- \(r\) the radius of the circular end
- \(h\) the height (the length between the two ends)
- \(2\pi rh\) the curved surface area: the label that wraps round a can
When to use it
For tins, pipes, tanks and any prism with a circular cross-section: the area of the circle πr² times the length h.
Worked example
A cylindrical water tank has radius 1.5 m and height 4 m. Find its volume.
- \(V=\pi(1.5)^2(4)=9\pi\)
Answer: \(V=28.3\text{ m}^3\) (3 s.f.)
Common mistake
Using the diameter as r. Halve the diameter first, and keep the units the same (convert m to cm before you multiply).
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
- Practise AI SL volume and surface area questions
- Revise 3D geometry (AI SL)
- Print AA SL one-page formula sheet
Questions
What is the volume of a cylinder formula?
The volume of a cylinder formula is V = πr²h (curved surface area = 2πrh). V: the volume; r: the radius of the circular end; h: the height (the length between the two ends); 2π rh: the curved surface area: the label that wraps round a can.
Is the volume of a cylinder 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 total surface area of a cylinder?
Total surface area = 2πrh + 2πr²: the curved surface plus the two circular ends. Leave out an end if the cylinder is open.
Our own wording, examples and card, checked by IB Math Revision. Not produced or endorsed by the International Baccalaureate Organization.