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Volume of a cylinder

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

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Student-friendly explanation

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.

How to write this in exams

  1. 1

    Start with the exact idea

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

  2. 2

    Then show how to use it

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

  3. 3

    Add one concrete example

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

  4. 4

    Avoid this incomplete answer

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

Definition

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

Example

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

Rule to remember

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

Memory hook

Base area times height gives volume.

Examples and method

Worked example

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

Method to apply

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

Diagram support

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.

How CBSE asks it

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

Avoid common mistakes

Common confusion

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

Common wrong answer

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

Exam tip

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

Quick check

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

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

Answer writing and exam use

1-mark answer

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

2-mark answer

The volume of a cylinder is the amount of space enclosed inside it. Volume of a cylinder = πr²h, where r is the radius of the base and h is the height. A cylinder with radius 7 cm and height 10 cm has volume πr²h = π × 49 × 10 = 490π cm³ = 1540 cm³.

3-mark answer

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. Volume of a cylinder = πr²h, where r is the radius of the base and h is the height. For r = 7 cm and h = 10 cm, volume = πr²h = π × 7² × 10 = 490π cm³ = 1540 cm³. Find the capacity of a cylindrical tank, drum, pipe section, or solid cylinder from given dimensions. A common wrong answer is to use 2πrh or 2πr(h+r). Those are surface area formulas, not volume formulas.
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