medium difficulty4 min

Area of Circle and Sector

The area of a circle is the surface inside its boundary, and the area of a sector is a fractional part of the circle's area.

In one line: Area fills the circle, so radius is multiplied twice.

Practice This Concept

Understand it

Circle area depends on the square of radius. A sector's area depends on the central angle, just as arc length depends on the same fraction of the full circle.

Formula and rule

Circle area = πr².

Sector area = θ/360 × πr², where θ is the central angle in degrees.

See it worked out

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

Worked example

1A sector has radius 14 cm and angle 45°.
2Area = 45/360 × 22/7 × 14 × 14 = 77 cm².

Method you can reuse

Identify radius, square it, multiply by π, and for a sector multiply by θ/360.

Visual tip

A circle or sector diagram should mark radius and central angle clearly.

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

What is the area of a circle of radius 10 cm using π = 3.14?

Think first, then show answer

The area is πr² = 3.14 × 10 × 10 = 314 cm² because area depends on the square of radius.

Common wrong answer

44 cm² for radius 7 cm.

Why it loses marks: 44 cm is circumference, not area.

Don't mix this up

Students use circumference formula when the question asks for the surface inside a circle.

Exam tip

Area uses square units and r²; circumference or arc length uses length units.

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

Questions may ask area of a circular park, sector-shaped sheet, shaded region, or a comparison with arc length.

1
Enough for 1 mark
The area of a circle is the surface inside its boundary, and the area of a sector is a fractional part of the circle's area.
2
Add for 2 marks
Example: For radius 7 cm, circle area = 22/7 × 7 × 7 = 154 cm². A 90° sector has area 90/360 × 154 = 38.5 cm².
3
Add for 3 marks
A sector's area depends on the central angle, just as arc length depends on the same fraction of the full circle.

MCQ Quiz

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