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Happy Monday 

Happy Monday . Please pick up the paper on the front table Tonight’s HW: P 767 #2-5, 9- 11 Finish notes. Agenda. Whiteboard Review 11.3 Sector Area and Arc Length Practice What if…?. Let’s Review!: Whiteboard. What is the formula for the area of a circle?

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Happy Monday 

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  1. Happy Monday  Please pick up the paper on the front table Tonight’s HW: • P 767 #2-5, 9-11 • Finish notes

  2. Agenda • Whiteboard Review • 11.3 Sector Area and Arc Length • Practice • What if…?

  3. Let’s Review!: Whiteboard What is the formula for the area of a circle? What is the formula for the circumference of a circle?

  4. Concept Review Total Measure of a Circle 360°

  5. Concept Review Circumference of a Circle

  6. Concept Review Area of a Circle

  7. Whiteboard • Find the area • Find the circumference

  8. Whiteboard • Find the area • Find the circumference

  9. Learning Objective By the end of the period you will be able to: • Use proportions to calculate the sector area and arc lengthof circles

  10. 11.3 Sector Area and Arc Length This entire semester we have been using ratios and proportions to demonstrate comparison between two quantities. Today we are going to use ratios and proportions to find sector area and arc length.

  11. Whiteboards Find the diameter of the pumpkin pie. The area of the pie is 9π cm2. Compare diameters with your partner.

  12. Whiteboards What if I am not that hungry and I only want a section of it? To be specific I only want 60°. This section we call our Sector. I challenge you and your partner to find the sector area of this 60° piece of a pumpkin pie. 60°

  13. Sector of a Circle • area of a piece of the circle (area between two radii and their arc). *Like a slice of pie.

  14. Steps to Find Sector Area • Divide the angle of the sectorby the total angle measure of a circle ( 360°) • Find the area of the whole circle. • Multiply the two together

  15. Which is basically writing a proportion!

  16. Example 1 Find the area of each sector. Give answers in terms of and rounded to the nearest hundredth. (a) sector HGJ(b) sector ABC

  17. Example 1 Find the area of each sector. Give answers in terms of and rounded to the nearest hundredth. (c) sector ACB

  18. Example 1(d) 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°?

  19. Math Joke of the Day! • What’s the difference between the diameter and the radius? • The radius!

  20. 11.3 Sector Area and Arc Length Now, let’s say I want to create a circular building. This building has one entrance only that creates a central angle of 50°. The radius of the building will be 125 feet. What is the arc length of the entrance? • If we are looking for arc length, what should our units be? • With your partner, discuss how you can possibly find the arc length.

  21. Arc Length • the distance among an arc measured in linear units. • The length of the crust of a pie

  22. Steps to Find Arc Length • Divide the angle of the arc by the total angle measure of a circle. • Find the circumference of the whole circle. • Multiply the two together

  23. This is basically writing a proportion!

  24. Example 2

  25. Example 2 (c): Find each arc length. Give answers in terms of  and rounded to the nearest hundredth. Circle with an arc measure of 62 in a circle with radius 2 m.

  26. Let’s Practice Take the next 5 minutes to complete the practice problems at the bottom of your guided notes. After the 10 minutes I will call on random students to share their solutions.

  27. Let’s Practice

  28. Let’s Practice

  29. Take out half sheet of paper..

  30. What if..? Your friend was absent. How would you summarize this lesson to him/her in 2-3 sentences? Write your summary.

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