A sector of a circle is a pie shaped portion of the area of the circle. Technically, the piece of pie is between two segments coming out of the center of the circle.

Let's review what we know about the area of circles and sectors.
Area of a circle

Area of sectors of circle
(Sectors are similar to "pizza pie slices" of a circle.)
Semi-circle
(half of circle = half of area)
Quarter-Circle
(1/4 of circle = 1/4 of area)

Any Sector
(fractional part of the area)
Area of sector =

Sector Activity
• 2 different colors of construction paper
• Use compass to draw the same circle on both pieces of construction paper ( be sure to mark centers )
• Cut out circles
• On one colored circle, draw a radius. Draw another radius to form an acute angle. Cut along these radii to “cut out the sector”
• Tape this cut up circle on top of the whole circle ( be sure to match up centers )

• Estimate the measure of your central angle and fill in measure on the circle
• Measure the length of your radius using cm and fill in measure on the circle
• We will calculate the area of your sector together using the formula
Area of sector =

Area of a sector of a circle Practice Problems
Calculate the area of each shaded sector. Write the answer two ways... one with pi and one as a decimal
Area of a Sector of a circle =
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Real World Application:
1. Suppose you stop at a small pizza shop for lunch.
The shop sells pizza by the slice. Each pizza is cut into eight equal pieces. You can afford two slices from a small pizza with the diameter of 10 inches or one slice from a large pizza with the diameter of 14 inches. Which will satisfy your hunger better?
Hints on next slide

Each pizza slice represents a geometric figure called a sector. A
sector is a region of a circle that is bounded by two radii and an arc of the circle. The area of the sector depends on the measure of the arc and the radius of the circle.
a. What is the area of one slice of the large pizza?
b. What is the area of two slices of the small pizza?

The formula for the arc length of a circle:
Arc Length = x 2 r

Arc length of a sector of a circle Practice Problems
Calculate the arc length of each shaded sector. Write the answer two ways... one with pi and one as a decimal
Arc length of a sector of a circle = x 2 π r
1.
2.
3.
4.