Key Concepts
- 1Area of sector
- 2Arc length
- 3Area of segment
- 4Area of circle
- 5Circumference
- 6Area of ring (annulus)
- 7Area of sector
- 8What is the formula for the area of a circle?
- 9What is the formula for the area of a sector of a circle?
- 10What is the area of a segment of a circle?
Important Formulas & Facts
#1
A = (θ/360°) × πr²
#2
l = (θ/360°) × 2πr
#3
= Area of sector - Area of triangle
#4
πr² or πd²/4
#5
2πr or πd
#6
π(R² - r²) where R > r
#7
A = (θ/360°) × πr²
#8
Area = pi x r^2, where r is the radius.
#9
Area of sector = (theta/360) x pi x r^2, where theta is the central angle in degrees.
#10
Area of segment = Area of corresponding sector - Area of the corresponding triangle = (theta/360) x pi x r^2 - (1/2) x r^2 x sin(theta).
Must-Know Questions
Q1Find the area of a sector with angle 60° and radius 14 cm.
Explanation
(60/360) × (22/7) × 196 = (1/6) × 616 = 308/3 cm².
Q2Circumference = 22 cm. Find area.
Explanation
2πr = 22 → r = 7/2. Area = (22/7)(49/4) = 77/2 = 38.5 cm².
Q3Circle radius 7 cm with 90° sector removed. Find remaining area.
Explanation
(270/360) × (22/7) × 49 = (3/4) × 154 = 115.5 cm².
Q4Minute hand 14 cm long. Area swept in 5 minutes.
Explanation
5 min = 30°. (30/360)(22/7)(196) = (1/12)(616) = 154/3 cm².
Q5Wire of circular radius 28 cm bent into square. Find area of square.
Explanation
Circumference = 2(22/7)(28) = 176 cm. Side = 44 cm. Area = 1936 cm².
Practice Areas Related to Circles
Reinforce what you just revised with practice questions