Unit 9. Day 8.

We want the area of the circle 𝐶=𝜋∙𝑑 𝐶 𝐶=𝜋∙ 2𝑟 2 𝐶 = 𝜋∙𝑟 𝜋∙𝑟 𝑟 𝑟 𝑟 2 We will find the area of this “rectangle” 𝐴= 𝜋∙ 𝑏∙ℎ 𝑙∙𝑤 ∙ 𝑟

Example A: Find the area of the circle. 𝜋≈3.1415926… 𝐴=𝜋∙ 𝑟 2 22 7 𝜋≈3.1415926… 𝜋 3.14 𝐴=𝜋∙ 𝑟 2 7 𝑐𝑚 7 𝑐𝑚 7 𝑐𝑚 7 𝑐𝑚 𝐴= ∙ 2 𝐴= 𝜋 ∙ 49 𝑐𝑚 2 𝐴=49𝜋 𝑐𝑚 2 𝐴=𝜋∙ 𝑟 2 𝐴=𝜋∙ 𝑟 2 𝐴= ∙ 2 𝐴= ∙ 2 𝐴≈ 22 7 ∙ 49 1 𝑐𝑚 2 7 49 𝑐𝑚 2 𝐴≈ 3.14 ∙ 49 𝑐𝑚 2 1 𝐴 ≈153.86 𝑐𝑚 2 𝐴≈154 𝑐𝑚 2

Example B: Find the area of the circle. 𝜋≈3.1415926… 𝐴=𝜋∙ 𝑟 2 22 7 𝜋≈3.1415926… 𝜋 3.14 𝐴=𝜋∙ 𝑟 2 4 𝑖𝑛 8 𝑖𝑛 4 𝑖𝑛 4 𝑖𝑛 𝐴= ∙ 2 𝐴= 𝜋 ∙ 16 𝑖𝑛 2 𝐴=16𝜋 𝑖𝑛 2 𝐴=𝜋∙ 𝑟 2 𝐴=𝜋∙ 𝑟 2 𝐴= ∙ 2 𝐴= ∙ 2 16 1 𝑖𝑛 2 𝐴≈ 22 7 ∙ 16 𝑖𝑛 2 𝐴≈ 3.14 ∙ 16 𝑖𝑛 2 𝐴≈ 352 7 𝑖𝑛 2 ≈50 2 7 𝑖𝑛 2 𝐴 ≈50.24 𝑖𝑛 2

Example C: A sprinkler rotates in a circular pattern and sprays water over a distance of 12 feet. What is the area of the circular region covered by the sprinkler? Express your answer to the nearest square foot. Example D: Suzanne is making a circular table out of a square piece of wood. The square is 6 ft by 6 ft, and Suzanne wants to cut as big a circle as possible. How much waste will she have for this project? Express your answer to the nearest square foot.

Example C: A sprinkler rotates in a circular pattern and sprays water over a distance of 12 feet. What is the area of the circular region covered by the sprinkler? Express your answer to the nearest square foot. 𝜋≈3.1415926… 3.14 𝐴=𝜋∙ 𝑟 2 𝐴= ∙ 2 𝐴≈ 3.14 ∙ 144 𝑓𝑡 2 𝐴 ≈452.16 𝑐𝑚 2 12 𝑓𝑡 12 𝑓𝑡

Example D: Suzanne is making a circular table out of a square piece of wood. The radius of the circle that she is cutting is 3 feet. How much waste will she have for this project? Express your answer to the nearest square foot. 𝐴= 36 𝑓𝑡 2 𝜋≈3.1415926… 3.14 𝐴=𝜋∙ 𝑟 2 6 𝑓𝑡 𝐴= ∙ 2 𝐴≈ 3.14 ∙ 9 𝑓𝑡 2 𝐴 ≈28.26 𝑓𝑡 2 3 𝑓𝑡 3 𝑓𝑡 6 𝑓𝑡 36 − 28.26 7.74 𝑓𝑡 2 ≈8 𝑓𝑡 2