C
CraftExam
medium difficulty5 min

Total surface area of a cylinder

The total surface area of a cylinder is the area of its curved surface plus the areas of both circular bases.

In one line: Total means side plus both ends.

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Understand it

A closed cylinder has three exposed parts: one curved side and two circular ends. When a question asks for the outer or total surface area, all these exposed parts must be counted together. This is why the formula combines the curved part and the two bases into one expression.

Example

For a closed cylinder with radius 3 cm and height 8 cm, TSA = 2πr(h+r) = 2π × 3 × (8+3) = 66π cm², which is 207.43 cm² approximately.

Formula and rule

Total surface area of a cylinder = 2πr(h+r), which is the curved surface area 2πrh plus the two base areas 2πr².

See it worked out

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

Worked example

For r = 3 cm and h = 8 cm, TSA = 2πr(h+r) = 2 × π × 3 × 11 = 66π cm².

Method you can reuse

  1. 1Check that the cylinder is closed or all outer surfaces are needed.
  2. 2Write TSA = 2πr(h+r).
  3. 3Substitute the given r and h.
  4. 4Simplify carefully.
  5. 5Write the final answer with square units.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

A closed cylindrical water tank is painted on every outer surface. Which formula should be used?

Think first, then show answer
Use 2πr(h+r), because the curved side and both circular bases are all part of the total outer surface.

Common wrong answer

A common wrong answer is 2πrh. That gives only the curved side and misses the two circular ends.

Don't mix this up

Students often forget one or both circular bases and write only the curved surface area.

Exam tip

When the cylinder is closed or all outer surfaces are mentioned, use 2πr(h+r).

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 total outer area of a closed cylindrical can, drum, tank, or pipe end-to-end surface.
  1. 1

    Enough for 1 mark

    The total surface area of a cylinder is the area of its curved surface plus the areas of both circular bases.

  2. 2

    Add for 2 marks

    Example: For a closed cylinder with radius 3 cm and height 8 cm, TSA = 2πr(h+r) = 2π × 3 × (8+3) = 66π cm², which is 207.43 cm² approximately.

  3. 3

    Add for 3 marks

    A closed cylinder has three exposed parts: one curved side and two circular ends.

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