medium difficulty5 min

Volume of a cylinder

The volume of a cylinder is the amount of space enclosed inside it.

In one line: Base area times height gives volume.

Understand it

A cylinder has the same circular cross-section throughout its height. So its volume is found by multiplying the area of the circular base by the height. This makes the formula simple and very useful in capacity questions like tanks, drums, and containers.

Example

A cylinder with radius 7 cm and height 10 cm has volume πr²h = π × 49 × 10 = 490π cm³ = 1540 cm³.

Formula and rule

Volume of a cylinder = πr²h, where r is the radius of the base and h is the height.

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

For r = 7 cm and h = 10 cm, volume = πr²h = π × 7² × 10 = 490π cm³ = 1540 cm³.

Method you can reuse

1Identify the radius and height.
2Square the radius first.
3Multiply by π and then by height.
4Simplify using the given value of π.
5Write the answer in cubic units.

Sketch it in your answer

Draw a cylinder with the radius marked on the base and the vertical height marked along the side. Show that every horizontal slice has the same circular area.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

A water tank is shaped like a cylinder. Which formula gives its capacity?

Think first, then show answer

Use πr²h, because the capacity of a cylinder is found by multiplying the circular base area by the height.

Common wrong answer

A common wrong answer is to use 2πrh or 2πr(h+r). Those are surface area formulas, not volume formulas.

Don't mix this up

Students often use surface area formulas instead of the volume formula, or they forget to square the radius.

Exam tip

For capacity or space inside a cylinder, always use πr²h and write cubic units.

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

Find the capacity of a cylindrical tank, drum, pipe section, or solid cylinder from given dimensions.

1
Enough for 1 mark
The volume of a cylinder is the amount of space enclosed inside it.
2
Add for 2 marks
Example: A cylinder with radius 7 cm and height 10 cm has volume πr²h = π × 49 × 10 = 490π cm³ = 1540 cm³.
3
Add for 3 marks
A cylinder has the same circular cross-section throughout its height.

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