1 / 29

Sectors, Segments, & Annuli

Sectors, Segments, & Annuli. Parts of Circles (and yes, you need to know this). We start with a circle. Then…. Sector. Segment. Annulus. Sector. Segment. Annulus. How do we find the areas of these?. We know the area of a circle. r. = radius. A = π r 2. So…. Sector. r.

jag
Télécharger la présentation

Sectors, Segments, & Annuli

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Sectors, Segments, & Annuli Parts of Circles (and yes, you need to know this)

  2. We start with a circle Then…

  3. Sector

  4. Segment

  5. Annulus

  6. Sector

  7. Segment

  8. Annulus

  9. How do we find the areas of these?

  10. We know the area of a circle r = radius A = πr2 So…

  11. Sector r = radius α Degrees: 360˚ - α Radians: 2π - α

  12. Sector Area of the Circle: A = πr2 r = radius α Degrees: 360˚ - α Radians: 2π - α Ratio of Sector to Circle: (degrees) α/360 (radians) α/2π

  13. Sector Radians: A = πr2 (α/2π) = πr2 (α/2π) =(α/2) r2 α r

  14. Sector Radians: A = ½ r2α α r Degrees: A = (α/360) πr2

  15. What’s the area of this sector? Hint: 90° is the same as π/2 radians 5 90°

  16. What’s the area of this sector? Ratio of the Sector: R = 90°/360° or R = (π/2)(1/2π) Area of the Circle: A = 52π 5 90° Area of the Sector: A = 52π(π/2)(1/2π) A = 52π(90°/360°) Answer: A = 25π/4

  17. Segment r = radius α Degrees: 360˚ - α Radians: 2π - α

  18. Segment Radians: A = ½ r2α r α Degrees: A = (α/360) πr2 Then…

  19. Segment Area of the Segment = Area of the Sector – Area of the Triangle b h r α Area of the Segment: A = ½ r2α – ½ bh (radians) A = (α/360) πr2 – ½ bh (degrees)

  20. What’s the area of this segment? Hint: 120° is the same as 2π/3 radians 8 5 120°

  21. What’s the area of this segment? Ratio of the sector: R = 120°/360° or R = (2π/3)(1/2π) R = 1/3 Area of the circle: A = 52π 8 5 120° Area of the sector: A = 25π(1/3) A = 25π/3 Then…

  22. What’s the area of this segment? Area of the Segment = Area of the Sector – Area of the Triangle h2 = 52 – 42 h2 = 25 – 16 h2= 9 h = 3 4 4 h 5 Area of the Triangle: A = ½ bh A = ½ (8)(3) = ½ 24 = 12 So…

  23. What’s the area of this segment? Area of the Sector = 25π/3 Area of the Triangle = 12 Answer: A = (25π – 36)/3 Area of the Segment: A = As - At A = 25π/3 – 12 = (25π/3) – (36/3)

  24. Annulus Area of outside circle: A = πr12 r2 r1 Area of inside circle: A = πr22

  25. Annulus Area of Annulus = Area of Outside Circle – Area of Inside Circle r2 r1 Area of Annulus: A = πr12 – πr22

  26. What’s the Area of this annulus? Area of outside circle: A = 32π = 9π Area of inside circle: A = 22π = 4π 2 3 Area of Annulus = Area of Outside Circle – Area of Inside Circle So…

  27. What’s the Area of this annulus? Area of Annulus : A = Ao - Ai A = 9π – 4π 2 3 Answer: A = 5π

  28. Questions?

  29. And now for the homework…

More Related