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Area of Circles and Sectors

Area of Circles and Sectors. Lesson 7.4A M.3.G.1 Calculate probabilities arising in geometric contexts (Ex. Find the probability of hitting a particular ring on a dartboard.)

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Area of Circles and Sectors

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  1. Area of Circles and Sectors Lesson 7.4A M.3.G.1 Calculate probabilities arising in geometric contexts (Ex. Find the probability of hitting a particular ring on a dartboard.) M.3.G.2 Apply, using appropriate units, appropriate formulas (area, perimeter, surface area, volume) to solve application problems involving polygons, prisms, pyramids, cones, cylinders, spheres as well as composite figures, expressing solutions in both exact and approximate forms M.3.G.3 Relate changes in the measurement of one attribute of an object to changes in other attributes (Ex. How does changing the radius or height of a cylinder affect its surface area or volume?) R.4.G.5 Investigate and use the properties of angles (central and inscribed) arcs, chords, tangents, and secants to solve problems involving circles

  2. Area of Circles • Formula for area of a circle: • A = πr2

  3. Example • Find the area of the given circle. 18mm

  4. Example • Given the endpoints of the diameter of a circle, find the area of the circle. Give your answer in terms of π. • STEPS: 1. Use the distance formula to find the length of the diameter. • 2. Halve the diameter to find the radius. • 3. Use the radius to find the area

  5. Example • Given the endpoints of the diameter of a circle, find the area of the circle. Give your answer in terms of π. Endpoints of the diameter are: (7, -3) and (-1, 12)

  6. Now You Try… • Given the endpoints of the diameter of a circle, find the area of the circle. Give your answer in terms of π. • Endpoints of the diameter: (10, 12) and (5, 24)

  7. Example • Given the circumference of a circle, find the area of the circle. Give your answer in terms of πand rounded to the nearest hundredth. • Circumference = 18 π miles

  8. Now You Try… • Given the circumference of a circle, find the area of the circle. Give your answer in terms of πand rounded to the nearest hundredth. • Circumference = 389.56 inches

  9. Comparing Radii and Areas • The radius of circle N is 3 times larger than the radius of circle P. Describe how the areas of the two circles compare.

  10. Vocabulary • Central Angle: An angle made by two radii • Arc: An unbroken part of a circle • Sector: A region bounded by a central angle and its intercepted arc • Chord: A segment whose endpoints lie on the circle • Segment: A region bounded by a chord and its intercepted arc

  11. Sector Area • Formula for area of a sector:

  12. 72 3 cm Example • Find the area of the shaded sector. Give your answer in terms of πand rounded to the nearest tenth.

  13. 7 cm Now You Try… • Find the area of the shaded sector. Give your answer in terms of πand rounded to the nearest tenth.

  14. 4 ft - = Area of Segments • Find the area of the shaded segment. Round your answer to the nearest tenth.

  15. 9 inches Now You Try… • Find the area of the shaded segment. Round your answer to the nearest tenth.

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