C
CraftExam
medium difficulty6 min

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.

In one line: Curved side only: 2πrh.

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Understand it

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.

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.

Formula and rule

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

See it worked out

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

Worked example

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

Method you can reuse

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

Sketch it in your answer

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.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

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

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

Common wrong answer

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

Don't mix this up

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

Exam tip

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

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 curved surface area of a cylindrical container, pipe, drum, or label region using the given radius and height.
  1. 1

    Enough for 1 mark

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

  2. 2

    Add for 2 marks

    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.

  3. 3

    Add for 3 marks

    A cylinder looks like a rolled rectangle with two circular ends.

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