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Curved surface area of a cylinder

The curved surface area of a cylinder is the area of only the side surface, excluding both circular bases.

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Student-friendly explanation

A cylinder looks like a rolled rectangle with two circular ends. If you cut the curved side and open it, it becomes a rectangle whose length is the circumference of the base and whose breadth is the height of the cylinder. That is why the curved surface area depends on radius and height, not on the base area.

How to write this in exams

  1. 1

    Start with the exact idea

    The curved surface area of a cylinder is the area of only the side surface, excluding both circular bases.

  2. 2

    Then show how to use it

    1. Identify the radius and height. 2. Check whether only the side is required. 3. Apply CSA = 2πrh. 4. Substitute values carefully. 5. Simplify with proper units.

  3. 3

    Add one concrete example

    A tin can with radius 7 cm and height 10 cm needs side covering only. The area needed is 2πrh = 2 × π × 7 × 10 = 140π cm², which is 440 cm² when π = 22/7.

  4. 4

    Avoid this incomplete answer

    A common wrong answer is 2πr(r+h). That is the total surface area, so it wrongly includes both circular ends.

Definition

The curved surface area of a cylinder is the area of only the side surface, excluding both circular bases.

Example

A tin can with radius 7 cm and height 10 cm needs side covering only. The area needed is 2πrh = 2 × π × 7 × 10 = 140π cm², which is 440 cm² when π = 22/7.

Rule to remember

Curved surface area of a cylinder = 2πrh, where r is the radius of the base and h is the height of the cylinder.

Memory hook

Curved side only: 2πrh.

Examples and method

Worked example

For a cylinder with r = 7 cm and h = 10 cm, CSA = 2πrh = 2 × π × 7 × 10 = 140π cm² = 440 cm².

Method to apply

1. Identify the radius and height. 2. Check whether only the side is required. 3. Apply CSA = 2πrh. 4. Substitute values carefully. 5. Simplify with proper units.

Diagram support

Draw a cylinder, mark the radius on the circular base, and mark the vertical height along the side. Shade only the curved band between the two bases.

How CBSE asks it

Find the curved surface area of a cylindrical container, pipe, drum, or label region using the given radius and height.

Avoid common mistakes

Common confusion

Students often use the total surface area formula and include the two circular ends even when only the side is required.

Common wrong answer

A common wrong answer is 2πr(r+h). That is the total surface area, so it wrongly includes both circular ends.

Exam tip

If the question says only the side, label, cover, or curved part, use 2πrh and do not add the bases.

Quick check

A paper label covers only the side of a cylindrical jar. Which formula should be used for the label area?

Use 2πrh, because the label covers only the curved side of the cylinder and does not include the two circular bases.

Answer writing and exam use

1-mark answer

The curved surface area of a cylinder is the area of only the side surface, excluding both circular bases.

2-mark answer

The curved surface area of a cylinder is the area of only the side surface, excluding both circular bases. Curved surface area of a cylinder = 2πrh, where r is the radius of the base and h is the height of the cylinder. A tin can with radius 7 cm and height 10 cm needs side covering only. The area needed is 2πrh = 2 × π × 7 × 10 = 140π cm², which is 440 cm² when π = 22/7.

3-mark answer

A cylinder looks like a rolled rectangle with two circular ends. If you cut the curved side and open it, it becomes a rectangle whose length is the circumference of the base and whose breadth is the height of the cylinder. That is why the curved surface area depends on radius and height, not on the base area. Curved surface area of a cylinder = 2πrh, where r is the radius of the base and h is the height of the cylinder. For a cylinder with r = 7 cm and h = 10 cm, CSA = 2πrh = 2 × π × 7 × 10 = 140π cm² = 440 cm². Find the curved surface area of a cylindrical container, pipe, drum, or label region using the given radius and height. A common wrong answer is 2πr(r+h). That is the total surface area, so it wrongly includes both circular ends.
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