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
Find the volume of a cone of radius 7 cm and height 24 cm. Use \(\pi=\tfrac{22}{7}\).
- \(V=\tfrac13\times\tfrac{22}{7}\times7^2\times24=\tfrac13\times22\times7\times24\)
Answer: \(V=1232\text{ cm}^3\)
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 |
|---|---|
| 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 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?
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 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 CBSE Math Revision. Not produced or endorsed by CBSE or NCERT.