Finding the Area of a Sector of a Circle

By the end of the lesson, you’ll be able to find the area of any sector and see how this concept applies to real-world situations.

1. Lesson 5 Area of a Sector CIRCLES: By: Mr. Roberto C. Discutido

2. MATH STANDARD: Derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector. Convert between degrees and radians.

3. Essential Questions: What is a sector? How do you find the area of a sector?

4. Learning Objective: Students will be able to find the area of a sector of a circle given its radius and central angle in degrees.

5. RECALL: Area of a Circle An area of a circle is the region occupied by the circle in two-dimensional plane. Area   The area of a circle can be found using the formula:   where denotes the area and represents the length of the radius of the circle.  

6. Finding the Area of a Circle A circle has a radius of 10 inches, what is its area in terms of ?   in   Solution: We use the formula:         in 2 Substitute 10 for   Simplify 10 2 = 100

7. What if we’re only given a certain portion of the circle, can we still find the area of that shaded region? Area?  

8. Students will do an Exploration Activity using Jamboard!  Think-Pair-Share Activity THINK – Think about your own response. PAIR – Discuss your responses with partner. SHARE – Share your answer with the class.

9. Sector of a Circle       A sector of a circle is the portion of the circle enclosed by two radii and an arc . The region is a sector of circle . It resembles a “pizza” slice.   How do we find an area of sector of a circle?

10. Explore and Discover!       360 o 180 o 90 o Circle Semi-Circle Quarter-Circle Any Sector   full circle Central ∠ = 360 o fractional part Half circle = of area   Central ∠ = 180 o fractional part circle = of area   Central ∠ = 90 o fractional part o             Central ∠ = o        

11. Ex# 1 : Area of a Sector What is the area of the shaded sector in terms of ?   Solution: Use the formula:           in 2    

12. Skills Check-Up! Find the area of each sector. Give your answers in terms of and rounded to the nearest hundredth.  

13. Ex# 2 : Area of a Sector What is the area of the shaded sector in terms of ?   Solution: Use the formula:                         cm 2  

14. Area of a Sector in Real Life One whole pizza is to be divided equally among 6 people, if it has a radius of 7 inches, what is the area of each slice of pizza in terms of ?   Solution: Use the formula:               in 2   360 o

15. The top and bottom ends of a wind-shield wiper blade are 34 in. and 14 in. from the pivot point, respectively. While in operation the wiper sweeps through 135 o . Find the area swept by the blade. Ex# 3 : Area of a Sector

16. Short Quiz A. Find the area of the shaded sector in terms of 𝜋. 1. 2. 3. B. Solve each situational problem involving the area of a sector. Express your answer in terms of 𝜋. 4. The diagram shows a lawn area covered by a water sprinkler. What is the area of the lawn that is covered by the sprinkler? 5. On a basketball court, the free throw lane is marked off geometrically. This area of the court is called the key and is topped by a semicircle that has a diameter of 12 feet. Find the area of the semicircle to the nearest square foot.