BellworkWhat is the arc length of an arc that travels through 50o of a circle with radius 15 units?Three consecutive numbers have a sum of 144 and a product of 110544. What are the three numbers?

14

No Clickers

BellworkWhat is the arc length of an arc that travels through 50o of a circle with radius 15 units?

14

13.10units

BellworkThree consecutive numbers have a sum of 144 and a product of 110544. What are the three numbers?

14

47,48, 49

Areas of Circles and Sectors

Section 11.5

The Concept Yesterday we talked about arc length, or the measure of a

portion of a circle Today we’re going to talk about how we find the area of a

portion of a circle.

Area of a CircleWe’ve already seen the area of a circle, which is given by the

formulaTheorem 11.9

A=πr2

r

Don’t forget our discussion

on when to use π

SectorsA sector is a piece of a circle that has a distinct area that can be

determined in a similar way to that of arc length

r

θ

2sec 360torA r

This is the amount of the circle that the

arc travels through

This is the area of circle

SectorsWhat is the area of the sector shown below

15

60

2sec 360

torA r

26015

360 Arc

2

1225

6

117.81

Arc

Arc units

On your OwnWhat is the area of the sector shown below

22

1102464.61units

On your ownWhat is the area of the sector shown below

10

200

2174.53units

On your ownWhat is the area of the sector shown below

11.595o

2176.6units

112o

On your ownGiven the arc lengths, what is the measure of the Area of the

sector (shown in green) below?

15

31.42 u

2333units

18.33 u

Practical ExamplePizza from Domino’s comes as a 16” cut into 8 slices. A Extra

Large pizza from D’Bronx comes as a 30” pizza cut into 12 slices. What is the ratio of the areas of a Domino’s slice to a D’Bronx slice?

8 8 4 3275 75 754

28Dominoes : 8

8

215 75D'Bronx :

12 4

Most Important Points• How to figure the area of a sector

Homework

11.5 Exercises1, 2-32 even, 37, 38