Worked example 1
Question: Find the area of a 90° sector of radius 14 cm. Use π=22/7.
Solution: Area=(90/360)×22/7×14²=(1/4)×616=154 cm².
What this chapter covers
Find arc lengths, sector areas, and minor or major segment areas, then combine these with perimeters in applied problems.
Sector and segment
A sector is the region bounded by two radii and an arc. A segment is bounded by a chord and its arc. Segment area equals sector area minus the triangle formed by the two radii and chord. For a major segment, subtract the minor segment from the full circle.
Units and diagrams
Use the central angle in degrees and keep units squared for area. The current syllabus restricts segment questions to central angles 60°, 90° and 120°. State whether the requested region is minor or major.
Key formulae: Sector area = (θ/360°)πr². Arc length = (θ/360°)2πr. Minor segment area = sector area − triangle area.
Worked examples: CBSE question patterns
These are original practice questions modeled on common board-exam patterns; they are not reproduced past-paper questions.
Worked example 2
Question: Find the area of a 60° minor segment of a circle of radius 6 cm.
Solution: Sector area=(60/360)π×36=6π. The triangle has two sides 6 and included angle 60°, so it is equilateral with area 9√3. Segment area=6π−9√3 cm².
Practical activity / investigation
Cut a paper circle into 12 equal sectors and rearrange them alternately to approximate a rectangle. Compare its base and height with πr and r; use the model to explain the circle-area formula before calculating a sector.
Record: Write the aim, materials, steps, observations and conclusion in your notebook. Follow teacher supervision for any classroom activity.
Quick practice with answers
Try each question before opening its solution.
Practice 1: Find the arc length for r=21 cm and θ=60°.
(60/360)×2π×21=7π=22 cm if π=22/7.
Practice 2: Find the area of a 120° sector of radius 3 cm.
(120/360)×π×9=3π cm².
Practice 3: What must be subtracted from a minor sector to get the minor segment?
The area of the triangle formed by the two radii and the chord.
Revision checklist
- Can I explain the key idea without memorising a worked solution?
- Have I selected the right formula and written units where needed?
- Can I show each algebraic or geometric step clearly?
- Can I check my answer by substitution, estimation or a diagram?
Aligned to the Class X Mathematics curriculum for 2026–27 and the NCERT Mathematics textbook. Always confirm any school-specific internal assessment with your teacher.