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 and the surface area of a sphere of radius 21 cm. Use \(\pi=\tfrac{22}{7}\).
- \(V=\tfrac43\times\tfrac{22}{7}\times21^3=38\,808\)
- \(A=4\times\tfrac{22}{7}\times21^2=5544\)
Answer: \(V=38\,808\text{ cm}^3\), \(A=5544\text{ cm}^2\)
Common mistake
Using the diameter as r. Halve the diameter first.
On your course
| Course | In the exam |
|---|---|
| Class 10 | Learn it: CBSE gives no formula booklet |
| Class 9 | Learn it: CBSE gives no formula booklet |
From our own CBSE Maths formula sheets, in our words.
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?
Class 10: learn it: CBSE gives no formula booklet. Class 9: learn it: CBSE gives no formula booklet. This comes from our own CBSE 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 CBSE Math Revision. Not produced or endorsed by CBSE or NCERT.