Volume of a cylinder formula: V = πr²h
The volume of a cylinder formula is V = πr²h, CSA = 2πrh, TSA = 2πr(r + h).
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 cylinder has radius 7 cm and height 10 cm. Find its volume and its curved surface area. Use \(\pi=\tfrac{22}{7}\).
- \(V=\tfrac{22}{7}\times7^2\times10=22\times7\times10\)
- \(\text{CSA}=2\times\tfrac{22}{7}\times7\times10=2\times22\times10\)
Answer: \(V=1540\text{ cm}^3\), \(\text{CSA}=440\text{ cm}^2\)
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 |
|---|---|
| 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 cylinder formula?
The volume of a cylinder formula is V = πr²h, CSA = 2πrh, TSA = 2πr(r + h). 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?
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 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 CBSE Math Revision. Not produced or endorsed by CBSE or NCERT.