FW 3.4: More Circle Practice Learning Target: I will find the area of circle by connecting to the area of a parallelogram. HW: Complete Inv. 3.4 WS, Title of Picture puzzle and CORRECT with the KEY. Warm Up: 1a. What is the constant of proportionality of the line represented by the equation 1b. What is the y-intercept of the line represented by the equation 2 3 y = x - 4 2 3 y = x - 4 2a. The radius of a circular pizza is 6 inches. What are its circumference and area?

2a. The radius of a circular pizza is 6 inches 2a. The radius of a circular pizza is 6 inches. What are its circumference and area? Circumference = dπ = 12π = 12 (3.14) = 37.7 inches Area =  πr² = 36π = 36 (3.14) = 113.1 square inches / 113.1 in.²

Optimal area for fixed perimeter occurs with the circle. D. Suppose that you have 12 meters of fencing and want to make a pen for your pet dog. Which shape, a square or a circle, would give more area? Explain. Hint: Remember our polygonal prisms and rice! Optimal area for fixed perimeter occurs with the circle.

Circle: 𝒄𝒊𝒓𝒄𝒖𝒎𝒇𝒆𝒓𝒆𝒏𝒄𝒆 𝒑𝒊 = 𝟏𝟐 𝟑.𝟏𝟒 ≈ 3.8 diameter d=2r 𝟑.𝟖 𝟐 ≈ 1.9 D. Suppose that you have 12 meters of fencing and want to make a pen for your pet dog. Which shape, a square or a circle, would give more area? Explain. Hint: Remember our polygonal prisms and rice! Square: the side lengths = 3 m. each area = 9m². Circle: diameter: 12/π ≈ 3.8 meters, radius ≈1.9meters, and area ≈11.3 m². Circle: 𝒄𝒊𝒓𝒄𝒖𝒎𝒇𝒆𝒓𝒆𝒏𝒄𝒆 𝒑𝒊 = 𝟏𝟐 𝟑.𝟏𝟒 ≈ 3.8 diameter d=2r 𝟑.𝟖 𝟐 ≈ 1.9 πr² ≈ 1.9 x 1.9 x 3.14 = 11.33m² Optimal area for fixed perimeter occurs with the circle.

Optimal area for fixed perimeter occurs with the circle. Hint: Remember our polygonal prisms and rice!  E. A rectangular lawn has a perimeter of 36 meters and a circular exercise run has a circumference of 36 meters. Which shape will give Rico’s dog more area to run? Explain. Optimal area for fixed perimeter occurs with the circle.

Optimal area for fixed perimeter occurs with the circle. D. Suppose that you have 12 meters of fencing and want to make a pen for your pet dog. Which shape, a square or a circle, would give more area? Explain. Hint: Remember our polygonal prisms and rice! Square: the side lengths = 3 m. each area = 9m². Circle: diameter: 12/π ≈ 3.8 meters, radius ≈1.9meters, and area ≈11.3 m². Optimal area for fixed perimeter occurs with the circle.  E. A rectangular lawn has a perimeter of 36 meters and a circular exercise run has a circumference of 36 meters. Which shape will give Rico’s dog more area to run? Explain. Rectangle (Square): side lengths = 9 meters each , area = 81m². Circle: 𝒄𝒊𝒓𝒄𝒖𝒎𝒇𝒆𝒓𝒆𝒏𝒄𝒆 𝒑𝒊 = 𝟑𝟔 𝟑.𝟏𝟒 ≈ 11.46 diameter d=2r 𝟏𝟏.𝟒𝟔 𝟐 ≈ 5.73 πr² ≈ 5.73 x 5.73 x 3.14 = 103.13m² Optimal area for fixed perimeter occurs with the circle.

Review Right Triangular Prisms – packet p. 5 HW: Complete Inv. 3.4 WS, Title of Picture puzzle and CORRECT with the KEY.