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7.7 Areas of Circles and Sectors

7.7 Areas of Circles and Sectors. Quick Review. What is the circumference of a circle?. What is the area of a circle?. The interior angle sum of a circle is ?. What is the arc length formula?. Sector of a Circle. Formula is very similar to arc length

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7.7 Areas of Circles and Sectors

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  1. 7.7 Areas of Circles and Sectors

  2. Quick Review • What is the circumference of a circle? • What is the area of a circle? • The interior angle sum of a circle is ? • What is the arc length formula?

  3. Sector of a Circle • Formula is very similar to arc length • Notation is slightly different! - The center pt is used when describing a sector. - The is not used for sectors.

  4. How can we find area, based on what we already know?

  5. Area of a sector =

  6. 1. Find the area of the shaded sector2. Find the arc length of the shaded sector.

  7. Segmentany ideas of how to find the shaded area?

  8. Finding the Area of a Segment of a Circle – = Area of Sector Area of Triangle Area of Segment minus equals

  9. Find the area of segment RST to the nearest hundredth. Step 1 Find the area of sector RST. Use formula for area of sector. Substitute 4 for r and 90 for m. = 4π m2

  10. Continued Find the area of segment RST to the nearest hundredth. Step 2 Find the area of ∆RST. ST = 4 m, and RS = 4m. = 8 m2 Simplify.

  11. Continued Find the area of segment RST to the nearest hundredth. Step 3 area of segment = area of sector RST – area of ∆RST = 4π – 8  4.57 m2

  12. A segment of a circle

  13. Finding the Area of a Segment Find the area of segment LNM to the nearest hundredth. Step 1 Find the area of sector LNM. Use formula for area of sector. Substitute 9 for r and 120 for m. = 27π cm2

  14. Step 2 Find the area of ∆LNM. Draw altitude NO. Continued Find the area of segment LNM to the nearest hundredth.

  15. Continued Find the area of segment LNM to the nearest hundredth. Step 3 area of segment = area of sector LNM – area of ∆LNM = 49.75 cm2

  16. Find the area of the shaded portion

  17. Find the area of the red portion Of the Tube Sign.

  18. Find the shaded area with r = 2 , 4 , & 10

  19. What is the Area of the Black part? 3cm 1cm 5cm

  20. If you have 2 circles A and B that intersect at 2 points and the distance between the centers is 10. What is the area of the intersecting region? A B 10

  21. Classwork Time - Go! Page 397 7 - 27 odd 31-33 36-38

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