7.2 – Sectors of Circles

Essential Question: How do you find the radius of a sector given its’ area

and arc length?

Sector of a Circle

• the region bounded by a central angle and its intercepted arc.

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 =

r2

360

2

360r

2

2

1r

sr2

1

Example

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

Example

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

Example

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

Example

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

Example

• A phonograph record with diameter 12 in. turns at 33 rpm. Find the distance that a point on the rim travels in one minute.

3

1