Area of a sector
The area of a sector is the part of a circle enclosed by two radii and the corresponding arc.
Practice This ConceptMain explanation
Teacher explanation
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.
Simple analogy
Sector area means fraction of the full circle's area.
Common confusion
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.
Study the area of a sector diagram carefully
Use the labelled diagram to keep area of a sector clear in short answers and revision.
What this diagram makes clear
This diagram keeps the labels and direction of area of a sector in the right order.
Where this helps in exams
Use this for labelled diagram work and short exam answers on area of a sector.
Revision cue
Revise area of a sector through the labels before writing the answer.
Answer writing and exam use
1-mark use
Write the exact meaning of area of a sector in one clean line.
2-mark use
Define area of a sector and add one example or condition.
3-mark use
Explain area of a sector, show the method or example, and mention the common mistake.
Practice this concept with focused MCQs
Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.
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