Volume of a sphere
The volume of a sphere is the amount of space enclosed inside it.
In one line: Sphere volume is four-thirds π times radius cubed.
Practice This ConceptUnderstand it
A sphere is completely round, so its volume depends only on the radius. The formula shows that volume grows very fast when radius increases, because the radius is cubed. This makes sphere volume questions especially important in three-dimensional mensuration.
Example
Formula and rule
Volume of a sphere = 4/3 πr³, where r is the radius of the sphere.
See it worked out
Follow the example line by line, then use the same method on new questions.
Worked example
For r = 3 cm, volume = 4/3 πr³ = 4/3 × π × 27 = 36π cm³.
Method you can reuse
- 1Identify the radius.
- 2Cube the radius.
- 3Multiply by 4/3 and π.
- 4Simplify the result.
- 5Write the answer in cubic units.
Check yourself
Answer the question in your head before opening the answer.
Try it yourself
A solid ball has radius 3 cm. Which expression gives its volume?
Think first, then show answerHide answer
Common wrong answer
A common wrong answer is to use 4πr². That gives surface area, not the space enclosed inside the sphere.
Don't mix this up
Exam tip
Write it in the exam
Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.
How CBSE asks it
- 1
Enough for 1 mark
The volume of a sphere is the amount of space enclosed inside it.
- 2
Add for 2 marks
Example: A sphere of radius 3 cm has volume 4/3 πr³ = 4/3 × π × 27 = 36π cm³, which is about 113.14 cm³.
- 3
Add for 3 marks
The formula shows that volume grows very fast when radius increases, because the radius is cubed.
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