1. 11.3 Area of Circles and Sectors

2. Section 11.3 ~ Areas of Circles and Sectors
Objectives: Be able to find the area of circles and sectors!!
Quick Review: Z L M N O
Name the following from circle Z.
Minor arc:
Major arc:
Semicircle:
Radius:
Diameter:
ON, NM, ML, OM, NL
OLM, OLN, MNL, MOL, NOL, NOM, NLM OL
OZ, NZ, MZ, LZ OL

3. Theorem
The equation for the Area of a Circle Area equals radius squared times pi.

4. Theorem
The equation for the Area of a Circle Area equals pi times radius squared.

5. Area of a Circle! More Vocab:
Find the area of each circle. Leave answers in terms of π.
14 in.
10 in.
12 in.
More Vocab:
Sector of a circle: A O B
sector AOB
region bounded by an arc and the two radii touching its endpoints

6. Definition of a Circle Sector
A circle sector is a fraction of the circle enclosed by two radii and an arc.

7. The Equation for the Area of a Sector

8. The Equation for the Area of a Sector

9. Sector CZD Sector BZC Sector BZA A Z B 18° D C 72°
Find the area of each sector. Leave answers in terms of π.
Sector CZD
Sector BZC
Sector BZA Z A D C B
72°
20 cm
18°

10. Find the Radius The Sector Area is 𝟏𝟓𝝅 𝑪𝒆𝒏𝒕𝒓𝒂𝒍 𝑨𝒏𝒈𝒍𝒆 𝒊𝒔 𝟏𝟓𝟎°
𝑆𝑒𝑐𝑡𝑜𝑟= 𝜃 360 ( 𝑟 2 𝜋)
𝑟 2 =15( 12 5 )→36
15𝜋= ( 𝑟 2 )𝜋
𝑟 2 =36→ 𝑟 2 =± 36
15= 𝑟 2
𝑟=6

11. Challenge Problems!
Find the area of each shaded region. Leave answers in terms of π.
15 cm
10 in.

12. Do you know your formulas?
Circumference:
Arclength:
Area:
Area of sector: