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Perimeter and Area of Circles and Sectors (9-2 and 11-3)

Perimeter and Area of Circles and Sectors (9-2 and 11-3). I CAN Find the circumference and area of a circle Find the arc length of a sector Find the area of a sector. Warm Up Find the unknown side lengths in each special right triangle. 1. a 30°-60°-90° triangle with hypotenuse 2 ft.

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Perimeter and Area of Circles and Sectors (9-2 and 11-3)

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  1. Perimeter and Area of Circles and Sectors (9-2 and 11-3) I CAN • Find the circumference and area of a circle • Find the arc length of a sector • Find the area of a sector

  2. Warm Up Find the unknown side lengths in each special right triangle. 1. a 30°-60°-90° triangle with hypotenuse 2 ft 2. a 45°-45°-90° triangle with leg length 4 in. 3. a 30°-60°-90° triangle with longer leg length 3m

  3. The irrational number  is defined as the ratio of the circumference C to the diameter d, or A circleis the locus of points in a plane that are a fixed distance from a point called the center of the circle. A circle is named by the symbol  and its center. Ahas radius r= ABand diameter d= CD. Solving for C gives the formula C = d. Also d = 2r, so C = 2r.

  4. Recall from your past years in Math the following formulas:

  5. Arc length is related to the circumference of a circle. It is a fraction of the circumference of the circle One way of finding arc length.

  6. Fold a sheet of notebook paper in half. You will be writing examples for circumference and arc length on the left half of the paper. Complete each of the examples on the following slides on your “foldable” notes. Draw and label your pictures correctly.

  7. Finding circumference and arc lengths I. Find the circumference ofP, “circle with center P.” C = 2r P ● 24 cm C = d C = 24  cm

  8. Finding circumference and arc lengths II. Find the arc length (L) of AB ●A “piece of the circumference” ●B P ● 24 cm You can use proportions to easily find the arc length. Part 90 = L Whole 360 24  Remember the circumference is 24  1 = L 4 24 4L = 24 Cross multiply to solve proportion L = 6 cm Don’t forget units!

  9. Finding circumference and arc lengths III. Find the arc length (L) of AB ●A “piece of the circumference” ●B 80º P ● 24 cm Part 80 = L Whole 360 24  L = 16 cm 3 Don’t forget units!

  10. Just likearc lengthis related to thecircumferenceof a circle, the area of a sector is related to the area of the circle. The area of a sector is a fraction of the area of the circle

  11. One way of finding area of a sector

  12. Refer back to your foldable notes. You will be writing examples for area of circle and area of sectors on the right half of the paper. Complete each of the examples on the following slides on your “foldable” notes. Draw and label your pictures correctly.

  13. Finding area of circles and area of sectors I. Find the area of P A = r2 24 c m ● P A = (12)2 A = 144 cm2 Don’t forget your units!

  14. Finding area of circles and area of sectors II. Find the sector area (S) of sector APB ●A “piece of the area” ●B P ● 24 cm You can use proportions to easily find the sector area Part 90 = S Whole 360 144  Remember the total area is 144  1 = S 4 144 4S = 144 Cross multiply to solve proportion S = 36 cm2 Don’t forget units!

  15. Finding the area of circles and area of sectors III. Find the sector area (S) of sector APB ●A “piece of the area” ●B 80º P ● 24 cm Part 80 = S Whole 360 144  S = 32 cm2 Don’t forget units!

  16. A segment of a circle is a region bounded by an arc and its chord.

  17. ON YOUR OWN Find each arc length. Give answers in terms of  and rounded to the nearest hundredth. FG  5.96 cm  18.71 cm

  18. =  m  4.19 m ON YOUR OWN Find each arc length. Give your answer in terms of and rounded to the nearest hundredth. GH

  19. ON YOUR OWN Find the area of each sector. Give answers in terms of and rounded to the nearest hundredth. sector HGJ = 52.4 m2  164.62 m2

  20. ON YOUR OWN Find the area of each sector. Give your answer in terms of  and rounded to the nearest hundredth. sector ACB = 0.25 m2  0.79 m2

  21. Lesson Quiz: Part I Find each measure. Give answers in terms of and rounded to the nearest hundredth. 1. area of sector LQM 7.5in223.56 in2 2. length of NP 2.5 in. 7.85 in.

  22. Lesson Quiz: Part II 3. The gear of a grandfather clock has a radius of 3 in. To the nearest tenth of an inch, what distance does the gear cover when it rotates through an angle of 88°? 4.6 in.

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