C
CraftExam
medium difficulty5 min

Area of a sector

The area of a sector is the part of a circle enclosed by two radii and the corresponding arc.

In one line: Sector area means fraction of the full circle's area.

Practice This Concept

Understand it

A sector is like a pizza slice. Its area depends on the central angle and the radius of the circle. If the angle becomes larger, the sector area also becomes larger because a bigger part of the circle is included.

Example

For a sector of angle 60° in a circle of radius 9 cm, area = 60/360 × π × 9² = 13.5π cm².

Formula and rule

Area of sector = (θ/360) × πr², where θ is the central angle in degrees and r is the radius.

See it worked out

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

Worked example

For θ = 120° and r = 6 cm, area = 120/360 × π × 36 = 12π cm² = 37.68 cm² if π = 3.14.

Method you can reuse

  1. 1Identify the central angle.
  2. 2Note the radius.
  3. 3Use area of sector = θ/360 × πr².
  4. 4Substitute carefully.
  5. 5Simplify and write square units.

Sketch it in your answer

Draw a circle, mark the centre, show the two radii, and label the central angle θ clearly on the sector.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

A sector has central angle 90° in a circle of radius 8 cm. What part of the full circle does it represent?

Think first, then show answer
It represents one-fourth of the full circle, because 90° out of 360° is 1/4. So its area is one-fourth of the area of the complete circle.

Common wrong answer

A common wrong answer is 36π cm² for the 120° sector of radius 6 cm when the student forgets to divide by 360.

Don't mix this up

Students often use the full circle area formula instead of taking only the fraction given by the angle.

Exam tip

Always check whether the figure is the full circle or only a part of it before using the formula.

Area of a sector diagram

Open full screen to read every label clearly.

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 sector in a circle, especially in pizza-slice, fan-blade, or pie-chart style problems.
  1. 1

    Enough for 1 mark

    The area of a sector is the part of a circle enclosed by two radii and the corresponding arc.

  2. 2

    Add for 2 marks

    Example: For a sector of angle 60° in a circle of radius 9 cm, area = 60/360 × π × 9² = 13.5π cm².

  3. 3

    Add for 3 marks

    A sector is like a pizza slice.

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