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Geometry Section 10-3
- 1. Section 10-3 Areas ofCircles and Sectors
- 2. Essential Questions • Howdo you find areas of circles? • How do you find areas of sectors of circles?
- 3. Vocabulary 1. Sector ofa Circle: 2. Segment of a Circle:
- 4. Vocabulary 1. Sector ofa Circle: A region of a circle created by an angle whose vertex is the center of the circle (similar to a slice of pie) 2. Segment of a Circle:
- 5. Vocabulary 1. Sector ofa Circle: A region of a circle created by an angle whose vertex is the center of the circle (similar to a slice of pie) 2. Segment of a Circle: The region of a circle bounded by an arc and a chord
- 6. Example 1 Fuzzy JeffCo. manufactures circular covers for outdoor umbrellas. If the cover is 8 inches longer than the umbrella on each side, find the area of the cover in square inches.
- 7. Example 1 Fuzzy JeffCo. manufactures circular covers for outdoor umbrellas. If the cover is 8 inches longer than the umbrella on each side, find the area of the cover in square inches. A = πr2
- 8. Example 1 Fuzzy JeffCo. manufactures circular covers for outdoor umbrellas. If the cover is 8 inches longer than the umbrella on each side, find the area of the cover in square inches. A = πr2 r = 72 2 + 8
- 9. Example 1 Fuzzy JeffCo. manufactures circular covers for outdoor umbrellas. If the cover is 8 inches longer than the umbrella on each side, find the area of the cover in square inches. A = πr2 r = 72 2 + 8 r = 36 + 8
- 10. Example 1 Fuzzy JeffCo. manufactures circular covers for outdoor umbrellas. If the cover is 8 inches longer than the umbrella on each side, find the area of the cover in square inches. A = πr2 r = 72 2 + 8 r = 36 + 8 r = 44 in.
- 11. Example 1 Fuzzy JeffCo. manufactures circular covers for outdoor umbrellas. If the cover is 8 inches longer than the umbrella on each side, find the area of the cover in square inches. A = πr2 r = 72 2 + 8 r = 36 + 8 r = 44 in. A = π(44)2
- 12. Example 1 Fuzzy JeffCo. manufactures circular covers for outdoor umbrellas. If the cover is 8 inches longer than the umbrella on each side, find the area of the cover in square inches. A = πr2 r = 72 2 + 8 r = 36 + 8 r = 44 in. A = π(44)2 A = 1936π
- 13. Example 1 Fuzzy JeffCo. manufactures circular covers for outdoor umbrellas. If the cover is 8 inches longer than the umbrella on each side, find the area of the cover in square inches. A = πr2 r = 72 2 + 8 r = 36 + 8 r = 44 in. A = π(44)2 A = 1936π A ≈ 6082.12 in2
- 14. Formula for Areaof a Sector A sector of a circle takes up a percentage of the circle. This percentage is calculated by taking the full circle (360º) and determining how many degrees the angle formed at the center takes up. Then, divide that new angle by 360º and multiply by the area of the circle.
- 15. Formula for Areaof a Sector A sector of a circle takes up a percentage of the circle. This percentage is calculated by taking the full circle (360º) and determining how many degrees the angle formed at the center takes up. Then, divide that new angle by 360º and multiply by the area of the circle. A = x 360 iπr2
- 16. Formula for Areaof a Sector A sector of a circle takes up a percentage of the circle. This percentage is calculated by taking the full circle (360º) and determining how many degrees the angle formed at the center takes up. Then, divide that new angle by 360º and multiply by the area of the circle. A = x 360 iπr2 x is the degree of the angle inside the arc
- 17. Example 2 A pumpkinpie is cut into 10 congruent pieces. If the radius of the pie is 4 inches, what is the area that one slice of the pie takes up in the pie tin?
- 18. Example 2 A pumpkinpie is cut into 10 congruent pieces. If the radius of the pie is 4 inches, what is the area that one slice of the pie takes up in the pie tin? A = x 360 iπr2
- 19. Example 2 A pumpkinpie is cut into 10 congruent pieces. If the radius of the pie is 4 inches, what is the area that one slice of the pie takes up in the pie tin? A = x 360 iπr2 360 10
- 20. Example 2 A pumpkinpie is cut into 10 congruent pieces. If the radius of the pie is 4 inches, what is the area that one slice of the pie takes up in the pie tin? A = x 360 iπr2 360 10 = 36°
- 21. Example 2 A pumpkinpie is cut into 10 congruent pieces. If the radius of the pie is 4 inches, what is the area that one slice of the pie takes up in the pie tin? A = x 360 iπr2 360 10 = 36° A = 36 360 iπ(4)2
- 22. Example 2 A pumpkinpie is cut into 10 congruent pieces. If the radius of the pie is 4 inches, what is the area that one slice of the pie takes up in the pie tin? A = x 360 iπr2 360 10 = 36° A = 1.6π A = 36 360 iπ(4)2
- 23. Example 2 A pumpkinpie is cut into 10 congruent pieces. If the radius of the pie is 4 inches, what is the area that one slice of the pie takes up in the pie tin? A = x 360 iπr2 360 10 = 36° A = 1.6π A ≈ 5.03 in2 A = 36 360 iπ(4)2
- 24. Example 3 Find thearea of the shaded sector. Round to the nearest hundredth.
- 25. Example 3 Find thearea of the shaded sector. Round to the nearest hundredth. A = x 360 iπr2
- 26. Example 3 Find thearea of the shaded sector. Round to the nearest hundredth. A = x 360 iπr2 A = 152 360 iπ(7.4)2
- 27. Example 3 Find thearea of the shaded sector. Round to the nearest hundredth. A = x 360 iπr2 A = 152 360 iπ(7.4)2 A ≈ 72.64 cm2
- 28. Example 3 Find thearea of the shaded sector. Round to the nearest hundredth.
- 29. Example 3 Find thearea of the shaded sector. Round to the nearest hundredth. A = x 360 iπr2
- 30. Example 3 Find thearea of the shaded sector. Round to the nearest hundredth. A = x 360 iπr2 A = 360 − 75 360 iπ(4.2)2
- 31. Example 3 Find thearea of the shaded sector. Round to the nearest hundredth. A = x 360 iπr2 A = 360 − 75 360 iπ(4.2)2 A = 285 360 iπ(4.2)2
- 32. Example 3 Find thearea of the shaded sector. Round to the nearest hundredth. A = x 360 iπr2 A = 360 − 75 360 iπ(4.2)2 A ≈ 43.87 in2 A = 285 360 iπ(4.2)2
- 33.
- 34. Problem Set p. 745#3-7 all, 9-25 odd “Nothing is impossible, the word itself says 'I'm possible’!” - Audrey Hepburn