1. Recall Area of a Circle A = r2
Topic 11-3 Circles and Sectors
Objectives:
Find the areas of circles, sectors, and segments of circles
Recall
Area of a Circle
A = r2

2. Real-world and Pizza 10-inch pizza 12-inch pizza
How much more pizza is in a 12 inch diameter pizza than in a 10 inch diameter pizza?
10-inch pizza
Radius = 10/2 = 5
Area = (5)2
= 25
12-inch pizza
Radius = 12/2 = 6
Area = (6)2
= 36
Difference in Area = 36 - 25 = 11  34.6 in2

3. Sectors of Circles Sector of a Circle:
region bounded by an arc of the circle and the two radii to the arcs endpoints
name by using one arc endpoint, the center of the circle, and the other arc endpoint
(AOB of Circle O) A
arc
radius B O
radius

4. Area and Sectors of Circles – (Foldable)
The area of a sector is a fractional part of the area of a circle.
The ratio of a sector’s area to a circle’s area is:
measure of the arc
360

5. Areas of Sectors - foldable
Find the area of the shaded sector. . .
area of shaded sector = 𝑥 𝜋 9 2
= • (81) 70
360
= 𝜋 ≈49.48

6. Areas of Sectors - example
Find the area of sector ACB. Leave your answer in terms of π . . .
area of sector ACB = • r 2
mAB
360
= • (6)2
100
360
= • 36 5 18
= 10
The area of sector ACB is m2.

7. Segments of a Circle
Part of the circle bounded by an arc and the segments joining the arc’s endpoints
Segment of a circle

8. Finding Area of a Segment of a Circle (foldable)- = - ? =

9. Areas of segments- foldable
Find the area of the shaded segment.
= • (6)2 Substitute. 90
360
= 9𝜋
area of sector AOB = • r Use the formula for area of sector.
mAB
Step 1: Find the area of sector AOB. A
Step 2: Find the area of ∆AOB. O B
Area of ∆ = 𝑏ℎ
= ∗6=18
Step 3: Subtract area of ∆AOB from area of sector AOB
Area of sector AOB = 9𝝅 - 18

10. Areas of segments - example
Find the area of the shaded segment. Round your answer to the nearest tenth.
Step 1: Find the area of sector AOB.
= • (24)2 Substitute.
120
360
= • = Simplify. 1 3
area of sector AOB = • r2 Use the formula for
area of a sector.
mAB

11. (continued) Step 2: Find the area of AOB.
You can use a 30°-60°-90° triangle to find the height h of AOB and AB.
24 = 2h hypotenuse = 2 • shorter leg
12 = h Divide each side by 2.
= 3 • 12 = longer leg = 3• shorter leg
AB = Multiply each side by 2. AB 2
AOB has base ft ft, or ft and height 12 ft.
A = bh Area of a triangle
A = ( )(12) Substitute 24 for b and 12 for h.
A = Simplify. 1 2

12. (continued)
Step 3: Subtract the area of AOB from the area of sector AOB
to find the area of the segment of the circle.
area of segment = –
Use a calculator.
To the nearest tenth, the area of the shaded segment is ft2.