Areas Related to Circles
Areas Related to Circles tests circumference, area, sector, arc length and segment. Questions often combine a sector with a triangle or ask for the area of a shaded region.
Core rules
- Circumference=2πr; area=πr².
- Arc length of a sector of angle θ: (θ/360)×2πr.
- Area of sector: (θ/360)×πr².
- Area of minor segment = area of sector − area of triangle formed by the two radii and the chord.
- Area of ring/annulus = π(R²−r²). Use π=22/7 when the question gives it or when dimensions are multiples of 7.
Worked example
A sector has radius 7 cm and angle 90°. Area=(90/360)×(22/7)×7²=(1/4)×154=38.5 cm². Arc length=(90/360)×2×(22/7)×7=(1/4)×44=11 cm.
Traps
Use the sector angle, not the remaining angle, unless the question asks for the major sector. For a segment, subtract the triangle area; do not use the sector area alone. Keep radius and diameter separate-using diameter in πr² is a common error. If π is not specified, either leave it in terms of π or use the value stated. Check whether the answer needs cm² or cm.