03-10-2025-Area of Sector Lesson
Presentation
•
Mathematics
•
6th - 8th Grade
•
Easy
Antoinette Norris Woodson
Used 2+ times
FREE Resource
17 Slides • 21 Questions
1
2
Draw
Solve this riddle.
3
Draw
Draw two straight lines through the box to end up with four sections, each containing three of each symbol.
4
● I can define the parts of a circle
● I can define and measure in a circle
● I can find the measure of segments of a circle
● I can discover the properties of tangent lines
● I can find the measure of angles inside and outside of a circle
● I can find missing measures of angles and arcs using circle theorems.
● I can find the length of an arc and area of a sector of a circle.
● I can explain radian angle measures in terms of a circular radius and
arc length
Objectives
5
I can calculate lengths of arcs and areas of sectors in circles.
Learning Target
6
Circle Vocab
7
The measure of an arc is the degree of the angle that intercepts the arc. Remember that the measure of an arc is a degree, not a distance.
https://study.com/academy/lesson/measure-of-an-arc.html
8
10
Arc length is literally the length of the arc of a portion of a circle.
This arc is a part of the total circumference of a circle.
This length is measured as a linear distance.
https://study.com/academy/lesson/arc-length-definition-equation.html
11
Draw
A runner completes a 60° section of a circular track with a 40-meter radius. How far do they run?
Show your process.
12
Draw
A runner completes a 45° section of a circular track with a 50-meter radius. How far do they run?
Show your process.
13
Draw
A Ferris wheel has a radius of 25 meters. A rider moves along a 90° arc. Find the arc length.
Solution:
Show your process.
14
Draw
A highway curve follows a 45° arc of a 200-meter radius. Find the arc length.
Show your process.
15
Draw
A bike tire has a radius of 14 inches. It rolls along a 30° arc. Find the arc length.
Show your process
16
Draw
A swing ride moves along a 75° arc with a radius of 18 feet. Find the arc length.
Show your process
17
Draw
A satellite dish has a radius of 15 meters and receives signals from a 60° sector. Find the arc length.
Show your process.
18
Sector
The region inside a circle lying between two radii of the circle.
19
Circumference for linear distance
Area of Circle for Area of Sector
20
Question: Where do we see sectors in real life?
Examples:
Pizza Slices 🍕 – The crust length is the arc, and the slice area is the sector.
Ferris Wheel Ride 🎡 – A Ferris wheel seat moves along an arc, and the space covered is a sector.
Highway Curves 🛣 – Roads designed with circular turns use sector area for construction planning.
23
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25
Math Response
Find the area of the sector.
Round to the nearest hundredth.
26
27
Math Response
Find the area of the sector. Round to the nearest hundredth.
28
29
Draw
A pizza has a radius of 10 inches. One slice has a central angle of 45°. What is the area of that slice?
Show your process.
30
Draw
A Ferris wheel has a radius of 20 meters. A rider moves along a 90° sector. Find the area of the sector.
Show your process.
31
Draw
A sprinkler sprays water in a 120° sector over a circular garden with a 6-meter radius. Find the area covered by water.
Show your process.
32
Draw
A curved road section follows a 135° sector with a radius of 50 meters. Find the area of the road section.
Show your process.
33
Draw
A survey pie chart has a 72° sector representing one category. If the radius is 8 cm, find the area of the sector.
Show your process
34
Draw
A wind turbine blade moves through a 60° sector with a radius of 30 meters. Find the area swept by the blade.
Show your process
35
Draw
A pivot irrigation system covers a 270° sector of a circular field with a 20-meter radius. Find the area of the irrigated land.
Show your process.
36
Draw
A spotlight illuminates a 120° sector on a stage with a radius of 5 meters. Find the lit area.
Show the process.
37
Draw
A park has a circular flower bed with a 75° sector. The radius is 10 m. Find the area.
Show your process.
38
Poll
What is your level of confidence of today's lesson?
Show answer
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