Geometry 7.9 Area of Circles & Sectors 14 3 Sector of a Circle - A region bounded by 2 radii of the...

8
Geometry_7.9_March 14 1 warm-up after 7.8: 1. Find the radius. 2. Find the length of AB 3. Find m QR Geometry 7.9 Area of Circles & Sectors Learning Target : I can evaluate the area of circles & sectors. [G.C.5]

Transcript of Geometry 7.9 Area of Circles & Sectors 14 3 Sector of a Circle - A region bounded by 2 radii of the...

Page 1: Geometry 7.9 Area of Circles & Sectors 14 3 Sector of a Circle - A region bounded by 2 radii of the circle and their intercepted arc. sector APB Area of sector degrees in arc Area

Geometry_7.9_March 14

1

warm-up after 7.8:

1. Find the radius. 2. Find the length of AB

3. Find m QR

Geometry 7.9 Area of Circles & Sectors

Learning Target:I can evaluate the area of circles & sectors. [G.C.5]

Page 2: Geometry 7.9 Area of Circles & Sectors 14 3 Sector of a Circle - A region bounded by 2 radii of the circle and their intercepted arc. sector APB Area of sector degrees in arc Area

Geometry_7.9_March 14

2

Area of a circle = π radius2

Area of a circle

** Remember to follow order of operations (do exponents before you multiply)

Acircle = π r2

The diameter of a circle is 11cm. Find the area. 1.

2. The area of a circle is 158.3 yd2. What is the diameter?

diameter = 2 x radius

= 14.2 yds

Page 3: Geometry 7.9 Area of Circles & Sectors 14 3 Sector of a Circle - A region bounded by 2 radii of the circle and their intercepted arc. sector APB Area of sector degrees in arc Area

Geometry_7.9_March 14

3

Sector of a Circle- A region bounded by 2 radii of the circle and their intercepted arc.

sector APB

Area of sector degrees in arc

Area of circle 360˚=

3. Find the area of the sectors formed by ∠HJK.H

˚

m

Area of Blue Sector

Area of Red Sector

Page 4: Geometry 7.9 Area of Circles & Sectors 14 3 Sector of a Circle - A region bounded by 2 radii of the circle and their intercepted arc. sector APB Area of sector degrees in arc Area

Geometry_7.9_March 14

4

4. Find the area of C.

5. Find the area of the shaded region.

6 ft

18 ft

3 circles in total

Area of circles = Ans.

Page 5: Geometry 7.9 Area of Circles & Sectors 14 3 Sector of a Circle - A region bounded by 2 radii of the circle and their intercepted arc. sector APB Area of sector degrees in arc Area

Geometry_7.9_March 14

5

Assignment:7.9 worksheet

Page 6: Geometry 7.9 Area of Circles & Sectors 14 3 Sector of a Circle - A region bounded by 2 radii of the circle and their intercepted arc. sector APB Area of sector degrees in arc Area

Geometry Name ______________________________ Pd. ___ 7.9AreaofCircles&Sectors Findtheareaofthecirclewiththegiveninformation.Roundtonearesthundredth.Show all work!1.radius=5cm 2.diameter=16ft 3.circumference=72.22mArea=_____________ Area=_____________ Area=_____________Determinetheradiusofthecirclewiththegivenarea.Roundtonearesthundredth.Show all work!4.Area=25𝜋cm2 5.Area=48ft2 Radius=_____________ Radius=_____________Findtheareaoftheshadedsectors.Roundtonearesthundredth.Show all work!6. 7. 8. Area=_____________ Area=_____________ Area=_____________Usethediagramtofindtheindicatedmeasure.Roundtonearesthundredth.Show all work!9.Areaof⊙𝑀=_____________ 10.Areaof⊙𝑀=_____________ 11.Radius=_____________

Page 7: Geometry 7.9 Area of Circles & Sectors 14 3 Sector of a Circle - A region bounded by 2 radii of the circle and their intercepted arc. sector APB Area of sector degrees in arc Area

Findtheareaoftheshadedregion.Roundtonearesthundredth.Show all work!12. 13. Area=_____________ Area=_____________ 14.Findthecircumference,arclength,areaofthecircleandareaofthesector.Show all work! Circumference=_________ArcLength=__________Areaof⊙=_____________Areaofsector=___________Review.15.Writetheequationofacirclewithcenter(6,–1)andradiusof10.________________________________________________16.Theequationofacircleis(x+4)2+y2=49.Thecenterwouldbe______________andtheradiuswouldbe________.Findthefollowingvalues.Show all work!17. 18.

x=_______ x=_______19. 20. 21.

x=_______

! mAB! =________˚ x=_______ y=_______

210˚

6

Page 8: Geometry 7.9 Area of Circles & Sectors 14 3 Sector of a Circle - A region bounded by 2 radii of the circle and their intercepted arc. sector APB Area of sector degrees in arc Area

Geometry 7.9 (Area of circles and sectors) Worksheet Answers1. 78.5 cm2 2. 200.96 ft2 3. (r ≈ 11.5) A ≈ 415.27 m2

4. 5 cm 5. 3.9 ft

6. 52.3 in2 7. 126.04 m2 8. 602.88 ft2

9. 84.02 m2 10. 66.04 cm2 11. (area ≈ 50) r ≈ 4 m

12. 21.5 cm2 13. 220.16 cm2

Area of Square – Area of Circle Area of Square – Area of 16(Circles)

14. C = 37.68 ft, arc length = 21.98 ft,

Area of ⨀ = 113.04 ft2, Area sector = 65.94 ft2

15. (x – 6)2 + ( y + 1)2 = 100

16. (–4, 0), r = 7

17. 110˚ 18. 14

19. 120˚ 20. 61˚ 21. x = 26, y =48