L.O. Students will be able to calculate the area of a sector of a circle, by working in small groups and completing an investigation. Standards: 6.G.8.

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L.O. Students will be able to calculate the area of a sector of a circle, by working in small groups and completing an investigation. Standards: 6.G.8 Text: Vocabulary: Sector, Central Angle Do Now: Determine the area of a circle, with a diameter of 4 cm. Present your answer to the nearest whole number.

The area of this circle is approximately 13 sq cm. Do Now: Determine the area of a circle, with a diameter of 4 cm. Present your answer to the nearest whole number. A = π r² Given: d = 4 cm Since r = ½d, r = 2 cm π ≈ 3.14 A = (3.14) (2)² A = (3.14) (4) A = 12.56 cm² The area of this circle is approximately 13 sq cm. B 4 cm

Quick Review 4 cm B What is the line segment AB called? What does it represent? What does the area of a circle represent? How many degrees are in a circle? Approximately what is the area of this circle? How does the area of this circle relate to its degrees? How many parts is the circle divided into? How many degrees are in each part? How does this affect the area of the circle? What is the area of the remaining circle? How can you prove, that the area of the remaining half circle is approximately 6.5 sq cm?

Try It ! 5 cm What is the given information in this ‘circle’? Name the given central angle in the circle. Take a moment to think of a way to determine the area of the given ‘circle’. Now turn to your partner and (the first person) share your idea. Allow the second person to share their idea. Class share of a couple of different ideas. Model / test a couple of the ideas. 5 cm

To find the area of the sector of a circle… Use the formula: Substitute: (3.14) (6)² (60 / 360) Evaluate: (3.14) (36) ( .167) 18.84 Write your answer. The are of the sector of this circle is approximately 19 sq cm. 6 cm 60°

To find the area of the sector of a circle (2nd method)… Determine the area of the whole circle: A = π r² Substitute and solve: (3.14) (6)² = 113.04 Set up a proportion: Evaluate and write your answer. (60) (113.04) = (360)(n) 6,782.4 = 360n 18.84 = n The area of the sector is approximately 19 sq cm. 6 cm 60°

Challenge C 3 in 132° B What do you need to know to determine the area of the shaded portion of the above circle? Work with your partner to determine the area of the shaded portion of this circle. Show your work on the given paper. After a few minutes of small group work, groups will be joined together to share ideas. Finally some of the students will be asked to present their work. A

Share What do we need to know to determine the area of a circle? What additional information do we need to determine the area of a sector of a circle? What steps would you need to follow to determine the area of the sector of a circle? Can you determine a formula to calculate the area of the sector of a circle? Students will be given a few minutes to record their thoughts in their notebooks. A few students will be asked to share and present their work.

Summary To determine the area of the sector of a circle:

To consider… Now that you know how to determine the area of the sector of a circle… how can you use that information to determine the length of the arc of the central angle?