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6th Grade Chapter 7: Multiplying and Dividing Fractions – Homework Feb -12 7.4 Circles and Circumference (p 280) a) Circumference (C) is the perimeter of a circle. (Perimeter is the distance around any shape). b) Diameter (d) is a line through the center of the circle. 1 c) Radius (r) is of the diameter. 2 d) Center Point is the middle of the circle. 1 Since the Radius (r) is x Diameter, the Diameter is also 2r or d =2r. 2 6th Grade Chapter 7: Multiplying and Dividing Fractions – Homework Feb -12 The formula for Circumference (C) = 𝝅d or 𝑪 = 𝝅𝟐𝒓. (The normal format for 𝐶 = 𝜋2𝑟 𝑖𝑠 𝑪 = 𝟐𝝅𝒓 ) 𝜋 is a symbol for Pi. It is a nonrepeating decimal. 𝟐𝟐 We approximate 𝜋 to be a value of: 3.14 or 𝟕 Feb 10- Homework: page 282 7-23 Odd. 7) Find the approximate circumference of a circle with a radius of .95 meters. C = ?, r=Radius = .95 d = Diameter = 2 * r 𝜋 ≈ value of 3.14 or 𝟐𝟐 d = 2 * .95 = 1.9 𝐶 = 2𝜋𝑟 𝑜𝑟 𝐶 = 𝜋𝑑 C = 2 * 3.14 * .95 or 𝟕 C = 3.14 x 1.9 = 5.96 9) d = 4 : 𝐶 = 𝜋𝑑 𝐶 = 3.14 𝑥 4 = 12.56 ≈ 𝟏𝟐. 𝟔 1 7 11) d = 23 = 3 𝑜𝑟 2.33 𝟐𝟐 7 22 𝐶 = 𝜋𝑑 𝐶 = 3.14 𝑥 2.33 𝑜𝑟 𝐶 = 𝟕 𝑥 3 ≈ 3 = 𝟕 13) r = 6, so d=12: 𝐶 = 𝜋𝑑 𝐶 = 3.14 𝑥 12 = 37.68 ≈ 𝟑𝟕. 𝟕 15) d = 8, so 𝐶 = 𝜋𝑑 𝐶 = 3.14 𝑥 8 = 25.12 ≈ 𝟐𝟓. 𝟏 17) d = 3.1, so 𝐶 = 𝜋𝑑 𝐶 = 3.14 𝑥 3.1 = 9.73 ≈ 𝟗. 𝟕 19) Find the measure of a circumference of a circle that has a diameter of 16.8 centimeters. 𝐶 = 𝜋𝑑 𝐶 = 3.14 𝑥 16.8 = 52.75 ≈ 𝟓𝟐. 𝟖 𝟏 𝟑 1 21) A bike has a large wheel in the front with a radius of 22 feet. How far does the bike travel with each rotation of the wheel? 1 5 2 𝑜𝑟 2 2 𝑟= 𝐶 = 2𝜋𝑟 𝑜𝑟 𝐶 = 𝜋𝑑: 𝑠𝑜, 𝟏 𝒅 = 𝟐 𝒙 𝟐 = 𝟓 𝒐𝒓 𝟐 𝒅=𝟐𝒙 𝟓 𝟐 =𝟓 𝐶 = 𝜋𝑑 = 3.14 𝑥 5 ≈ 15.7 Or 𝐶 = 2𝜋𝑟 = 2 𝑥 𝟐𝟐 𝟕 𝒙 𝟓 𝟐 = 𝟐 𝒙 𝟐𝟐 𝒙 𝟓 𝟏𝒙𝟕𝒙𝟐 = 𝟏𝟏𝟎 𝟕 = 𝟏𝟓 23) Compare how the circumference of two circles compare if the diameter of 1 circle is twice the diameter of the other. C= 𝜋𝑑 Use 1 and 2: 3.14 x 1 vs 3.14 x 2 = 3.14 vs 6.28 Use 10 and 20: 3.14 x 10 vs 3.14 x 20 = 31.40 vs 62.8 Use 5 and 10: 3.14 x 5 vs 3.14 x 10 = 15.70 vs 31.4 𝟓 𝟕