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
A ball has diameter 12 cm. Find its volume.
- \(r=6\)
- \(V=\tfrac43\pi(6)^3=288\pi\)
Answer: \(V=905\text{ cm}^3\) (3 s.f.)
Common mistake
Using the diameter as r. Halve the diameter first.
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 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?
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 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 IB Math Revision. Not produced or endorsed by the International Baccalaureate Organization.