Mathematics · Class 10
Areas Related to Circles
Areas of sectors and segments of circles.
3 sections15–25 min read6 MCQs · 2 examples
Chapter Overview
Areas Related to Circles covers perimeter and area of circles, lengths of arcs, and areas of sectors and segments — applied to wheels, pulleys, and shaded-region problems.
Circle and Sector Formulas
Circumference
C = 2πr
Area of circle
A = πr²
Arc length
l = (θ/360°) × 2πr
Sector area
A = (θ/360°) × πr²
Segment and Composite Figures
- Segment area = sector area − triangular area
- For minor segment: subtract triangle from sector
- Shaded region = difference or sum of standard figures
- Use symmetry in semicircle and quadrant problems
Solved Examples
Step-by-step solutions — read each step before checking the final answer.
Example 1: Sector area
Find area of sector with r = 14 cm, θ = 90°.
- 1A = (90/360) × π × 14²
- 2= ¼ × π × 196 = 49π cm²
Answer
49π cm² ≈ 154 cm²
Example 2: Arc length
Arc subtends 60° at centre, r = 21 cm. Find arc length.
- 1l = (60/360) × 2π × 21
- 2= (1/6) × 42π = 7π cm
Answer
7π cm
Key Points to Remember
- ✓ θ is central angle in degrees unless stated radians
- ✓ Semicircle: θ = 180°, area = ½πr²
- ✓ Quadrant: θ = 90°
Exam Tips
- • Write θ/360 before substituting
- • Leave answer in terms of π unless told otherwise
- • Label sector vs segment clearly
Practice MCQs — Areas Related to Circles
Test your understanding with topic-wise multiple choice questions. Explanations appear after each answer.
Question 1 of 6Score: 0/0
Area of circle radius 7 cm is: