Lesson 52 Arc Length & Area of Sectors
In your groups, find the area of the shaded regions.
210o 5 cm 5 cm 5 cm Lesson 52 Arc Length & Area of Sectors
Objectives
Find circular arc length and areas of sectors.
Solve problems involving lengths of arcs or areas of sectors. Lesson 52 Arc Length & Area of Sectors
Lesson 52: Arc Length & Area of Sectors
Before we can calculate the length of arcs on a circle and the area of a sector of a circle, we need to recall a couple of formulas. Under each of the headings, write out the formula that is asked for.
Circumference of a Circle Area of a Circle
C = 2πr A = πr2
disk the union of a circle and its interior
sector of a circle part of a disk that is on or in the interior of a central angle. Lesson 52 Arc Length & Area of Sectors
Circular Sector Area Formula If A is the area of a sector formed by a central angle of Ѳ (radians or degrees) in a circle of radius r, then Lesson 52 Arc Length & Area of Sectors
Circular Arc Length Formula If s is the length of the arc of a central angle of Ѳ (radians or degrees) in a circle of radius r, then Lesson 52 Arc Length & Area of Sectors
Example 1 Find the length of an arc of a 135o central angle in a circle of radius 12ft.
135o 12ft Lesson 52 Arc Length & Area of Sectors
Example 2 A sector has a central angle measure of π/3 and a radius of 5cm. Draw a picture to represent the situation. Then find the arc length and area of the sector. Lesson 52 Arc Length & Area of Sectors
Example 3 A sprinkler with a radius of 20 meters can water 400 π/9 m2 of land in 30 minutes. Find the central angle and the time needed for the sprinkler to complete a full revolution. Lesson 52 Arc Length & Area of Sectors
Group Practice Problems Answers Lesson 52 Arc Length & Area of Sectors
Homework Lesson 52 p.276 #119 skip 911,13