Warm Up• RECALL: What is the formula for the area of a circle?• You eat an entire pizza (8 slices) with a radius of

8inches.• How much pizza (area) did you eat?

• If you only ate 4 slices, how much pizza did you eat?

• If you only ate 1 slice, how much pizza did you eat?

11.3: Area of a SectorArc Length and Area of a Sector

Objectives

• I will be able to…•Calculate the area of a sector in a circle•Determine the measure of an arc or the radius based on the area of the sector

• In the first picture, a slice of pizza represents a sector of the pizza.

• What is a sector for the other pictures?

Sector

Area of a Sector• The area of a sector is a fraction of a circle’s area.

Area of Sector = fraction of circle * area =

Find the area of sector XYZ to

the nearest tenth.

X

ZY

A ≈ 142.5 m2

135°11m

If the area of sector is 34 m2 and the radius is 6m, find the central angle to the nearest degree.

mÐD ≈ 108°

E

F

O

D

Homework:

• pg. 801 #19-20, 24, 28-29, 35

Partner Exit Slip!Arc Length or Sector Area?• With your partner, answer the following questions on a

half sheet of paper before you leave:

• #1: A windshield wiper blade is 18 inches long. To the nearest square inch, what is the area covered by the blade as it rotates through an angle of 122°? **Draw a picture of this situation**

• #2: A bicycle chain is shown at the left,which travels around the front and rearsprocket. The circumference of eachsprocket is shown. What is the lengthof the entire chain?

Homework Answers: 10.1-10.2, 11.3

pg. 701-70410.) R 11.) SU 12.) No; it’s a chord 13.) 8.1cm 19.) 14.6 20.) 12.6 27.) 830.23m; 415.12m 29.) 12π ft 31.) 10π in

pg. 710-71313.) 225˚ 15.) 40˚ 17.) minor; 125˚ 19.) major; 305˚ 21.) semi; 180˚ 23.) major; 270˚ 27.) 60˚ 29.) 300˚ 31.) 180˚ 33.) 220˚ 35.) 120˚ 61.) 175

pg. 71137.) 8.80cm 38.) 4.75mm 39.) 17.02in 40.) 19.01ft 46.) 150˚ 47.) 9.50ft

pg. 80119.) 40.2cm2 20.) 167.1ft2 24.) 28.) 55 29.) 9.8ft 35.) 10.7cm2