C
CraftExam
medium difficulty5 min

Area of a circle

The area of a circle is the amount of surface covered by the circular region inside its boundary.

In one line: Radius first, then square; circle area is inside share.

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Understand it

Area tells us how much flat space is enclosed by the circle. It is always written in square units such as cm², m², or mm². The radius is the most important value for finding circle area, because the formula depends directly on r.

Example

If a circle has radius 7 cm, its area is πr² = 49π cm², which is 154 cm² using π = 22/7.

Formula and rule

Area of circle = πr², where r is the radius.

Use square units because area measures surface.

See it worked out

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

Worked example

For r = 10 cm, area = π × 10² = 100π cm² = 314 cm² when π = 3.14.

Method you can reuse

  1. 1Identify the radius.
  2. 2Square the radius carefully.
  3. 3Multiply by π.
  4. 4Use the value of π given in the question or standard value.
  5. 5Write the final answer in square units.

Sketch it in your answer

Draw a circle and shade the interior region to show that area refers to the inside space, not the boundary.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

A circular pond has radius 4 m. What quantity does the area of the pond measure?

Think first, then show answer
The area measures the surface inside the circular boundary of the pond. For radius 4 m, you use πr² to find how much flat space the pond covers.

Common wrong answer

A common wrong answer is 31.4 cm² for radius 10 cm when the student multiplies π by 10 instead of 10².

Don't mix this up

Students sometimes use diameter instead of radius, or forget to square the radius before multiplying by π.

Exam tip

When the question asks for space covered, surface area, or carpet-like covering, use area of a circle.

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 area of a circular region, compare two circles by area, or find radius when area is given.
  1. 1

    Enough for 1 mark

    The area of a circle is the amount of surface covered by the circular region inside its boundary.

  2. 2

    Add for 2 marks

    Example: If a circle has radius 7 cm, its area is πr² = 49π cm², which is 154 cm² using π = 22/7.

  3. 3

    Add for 3 marks

    Area tells us how much flat space is enclosed by the circle.

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