Arc length and Sector area

Arc length and Sector area

Example

Find the area of the sector in terms of π if radius is 2 cm and angle subtended is 60°.

180° = π radians

θ = 60° = π/3 radians

r = radius = 2

Area = (1/2) r² θ

= (1/2) x 2² x π/3

= 2π/3 cm²

Example

Find the perimeter of the sector in terms of ∏ if the radius is 1 cm and angle subtended is 60°.

180° = π radians

θ = 60° = π /3 radians

r = radius = 1 cm

Arc Length = rθ

= 1 x π/3 = π/3 cm

Perimeter = π/3 + 1 + 1

= (π/3 + 2) cm

Questions

1. Find the arc length, perimeter and area of the sector in terms of π if radius is 12 cm and angle subtended is 60°.
2. Find the arc length, perimeter and area of the sector if radius is 5cm and angle subtended is 120°.