01 · BASIC FORMULAS
Perimeter & Area of a Circle
Perimeter (Circumference) = 2πr (or πd)Area of Circle = πr²
02 · SECTOR FORMULAS
Sector of a Circle & Arc Length
A sector is the portion of a circular region enclosed by two radii and their corresponding arc.
GEOMETRIC DIAGRAM
Minor Sector vs Major Sector
Area of Minor Sector = (θ / 360°) × πr²
Length of Arc APB = (θ / 360°) × 2πr
Area of Major Sector = πr² - Area of Minor Sector
Length of Arc APB = (θ / 360°) × 2πr
Area of Major Sector = πr² - Area of Minor Sector
03 · SOLVED NCERT EXAMPLES
Step-by-Step Problem Solving
EXAMPLE 1
Find the area of a sector of a circle with radius 6 cm if angle of sector is 60°
Given: radius r = 6 cm, angle θ = 60°.
Area = (θ / 360°) × πr²
Area = (60° / 360°) × (22/7) × 6 × 6
Area = (1 / 6) × (22/7) × 36 = 132 / 7 = 18.86 cm² (or 132/7 cm²)
Area = (60° / 360°) × (22/7) × 6 × 6
Area = (1 / 6) × (22/7) × 36 = 132 / 7 = 18.86 cm² (or 132/7 cm²)
EXAMPLE 2
Find the length of an arc of a circle of radius 21 cm which subtends an angle of 60° at center
Given: radius r = 21 cm, angle θ = 60°.
Arc Length = (60° / 360°) × 2 × (22/7) × 21
Arc Length = (1 / 6) × 2 × 22 × 3 = 22 cm
Arc Length = (1 / 6) × 2 × 22 × 3 = 22 cm
04 · QUICK SUMMARY
Key Takeaways
01
Area of sector: (θ/360°) × πr².
02
Length of arc: (θ/360°) × 2πr.
03
Major sector area = Total Circle Area - Minor Sector Area.