1. 7.2 – Sectors of Circles
Essential Question: How do you find the radius of a sector given its’ area and arc length?

2. Sector of a Circle
the region bounded by a central angle and its intercepted arc.

3. Formulas for Arc Length and Area of a Sector:
Degrees
Radians
Arc Length of a Sector
s =
s = r θ
Area of a Sector
K =
K =
or K =

4. Example
A sector of a circle has radius 6 cm and central angle .5 radians. Find its arc length and area.

5. Example
A sector of a circle has central angle 30° and arc length 3.5 cm. Find its area. Round to the nearest hundredth.

6. Example
A sector of a circle has area 88 cm2 and central angle 0.4 radians. Find its radius and arc length.

7. Example
A sector of a circle has perimeter 16 cm and area 15 cm2. Find all possible radii and arc lengths.

8. Example
A phonograph record with diameter 12 in. turns at rpm. Find the distance that a point on the rim travels in one minute.