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.

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Lesson 7.4B 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.

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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

Area of Circles Formula for area of a circle: Formula for area of a circle: A = π r 2 A = π r 2

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

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

Example Given the endpoints of the diameter of a circle, find the area of the circle. Give your answer in terms of π. 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)

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. 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) Endpoints of the diameter: (10, 12) and (5, 24)

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

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

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. The radius of circle N is 3 times larger than the radius of circle P. Describe how the areas of the two circles compare.

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

Sector Area Formula for area of a sector: Formula for area of a sector:

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

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

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

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