1. Section 7-2 Sectors of Circles SAS

2. Definition A sector of a circle is the region bounded by a central angle and the intercepted arc.

3. Symbols s = arc length of sector θ = central angle r = radius of circle K = area of sector

4. Arc Length and Area of Sectors In degrees: s = ∙ 2πr K = ∙ πr 2

5. Arc Length and Area of Sectors In radians: s = r θ K = rs or K = r 2 θ

6. Ex. 1: A sector of a circle has radius 6 cm and central angle 0.5 radians. Find its arc length and area. r = 6 cm θ = 0.5 radians s = rθ s = 6(0.5) s = 3 cm K = ½r 2 θ K = ½(6) 2 (.5) K = ½(18) K = 9 cm 2

7. Ex. 2: A sector of a circle has arc length 6 cm and area 75 cm 2. Find its radius and the measure of its central angle (in radians). s = 6 cmK = 75 cm 2 K = ½rs 2K = rs = r r = 25 cm s = rθ θ = θ = 0.24

8. Ex. 3: A sector of a circle has central angle 30º, arc length 3.5 cm, and radius 11.48 cm. Find its area to the nearest square centimeter. θ = 30º s = 3.5 cm r = 11.48 K = ∙ πr 2 K = ∙ (π)(11.48) 2 K = 34.50 cm 2

9. HOMEWORK pg. 264 – 265; 2 – 8 even