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9-8 Circles and Circumference Course 1 Warm Up Warm Up Lesson Presentation Lesson Presentation Problem of the Day Problem of the Day

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Warm Up The length and width of a rectangle are each multiplied by 5. Find how the perimeter and area of the rectangle change. The perimeter is multiplied by 5, and the area is multiplied by 25. Course 1 9-8 Circles and Circumference

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Problem of the Day When using a calculator to find the width of a rectangle whose length one knew, a student accidentally multiplied by 20 when she should have divided by 20. The answer displayed was 520. What is the correct width? 1.3 Course 1 9-8 Circles and Circumference

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Learn to identify the parts of a circle and to find the circumference of a circle. Course 1 9-8 Circles and Circumference

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Vocabulary circle center radius (radii) diameter circumference pi Insert Lesson Title Here Course 1 9-8 Circles and Circumference

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A circle is the set of all points in a plane that are the same distance from a given point, called the center. Center Course 1 9-8 Circles and Circumference

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A line segment with one endpoint at the center of the circle and the other endpoint on the circle is a radius (plural: radii). Center Radius Course 1 9-8 Circles and Circumference

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A diameter is a line segment that passes through the center of the circle and has both endpoints on the circle. The length of the diameter is twice the length of the radius. Center Radius Diameter Course 1 9-8 Circles and Circumference

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Additional Example 1: Naming Parts of a Circle Name the circle, a diameter, and three radii. N The circle is circle Z.LM is a diameter.ZL, ZM, and ZN are radii. M Z L Course 1 9-8 Circles and Circumference

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Check It Out: Example 1 Name the circle, a diameter, and three radii. The circle is circle D. IG is a diameter.DI, DG, and DH are radii. G H D I Course 1 9-8 Circles and Circumference

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The distance around a circle is called the circumference. Center Radius Diameter Circumference Course 1 9-8 Circles and Circumference

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The ratio of the circumference to the diameter,, is the same for any circle. This ratio is represented by the Greek letter , which is read “pi.” C d C d = Course 1 9-8 Circles and Circumference

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The decimal representation of pi starts with 3.14159265... and goes on forever without repeating. We estimate pi using either 3.14 or. 22 7 Course 1 9-8 Circles and Circumference

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Formula to find the circumference of a circle: C = d (d is the diameter) Or C= 2 r (r is the radius) USE 3.14 for . Course 1 9-8 Circles and Circumference

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Additional Example 2: Application A skydiver is laying out a circular target for his next jump. Estimate the circumference of the target by rounding to 3. C = dC 3 8C 24 ft Write the formula. Replace with 3 and d with 8. 8 ft Course 1 9-8 Circles and Circumference

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Check It Out: Example 2 A second skydiver is laying out a circular target for his next jump. Estimate the circumference of the target by rounding to 3. C = dC 3 14C 42 yd Write the formula. Replace with 3 and d with 14. 14 yd Course 1 9-8 Circles and Circumference

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Additional Example 3A: Using the Formula for the Circumference of a Circle Find the missing value to the nearest hundredth. Use 3.14 for pi. d = 11 ft; C = ? C = dC 3.14 11C 34.54 ft Write the formula. Replace with 3.14 and d with 11. 11 ft Course 1 9-8 Circles and Circumference

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Additional Example 3B: Using the Formula for the Circumference of a Circle Find each missing value to the nearest hundredth. Use 3.14 for pi. r = 5 cm; C = ? C = 2rC 2 3.14 5C 31.4 cm Write the formula. Replace with 3.14 and r with 5. 5 cm Course 1 9-8 Circles and Circumference

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Additional Example 3C: Using the Formula for the Circumference of a Circle Find each missing value to the nearest hundredth. Use 3.14 for pi. C = 21.98 cm; d = ? C = d 21.98 3.14d7.00 cm d Write the formula. Replace C with 21.98 and with 3.14. 21.98 3.14d _______ 3.14 3.14 Divide both sides by 3.14. Course 1 9-8 Circles and Circumference

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Check It Out: Example 3A Find the missing value to the nearest hundredth. Use 3.14 for pi. d = 9 ft; C = ? C = dC 3.14 9C 28.26 ft Write the formula. Replace with 3.14 and d with 9. 9 ft Course 1 9-8 Circles and Circumference

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Check It Out: Example 3B Find each missing value to the nearest hundredth. Use 3.14 for pi. r = 6 cm; C = ? C = 2rC 2 3.14 6C 37.68 cm Write the formula. Replace with 3.14 and r with 6. 6 cm Course 1 9-8 Circles and Circumference

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Check It Out: Example 3C Find each missing value to the nearest hundredth. Use 3.14 for pi. C = 18.84 cm; d = ? C = d 18.84 3.14d6.00 cm d Write the formula. Replace C with 18.84 and with 3.14. 18.84 3.14d _______ 3.14 3.14 Divide both sides by 3.14. Course 1 9-8 Circles and Circumference

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Lesson Quiz Find the circumference of each circle. Use 3.14 for . 1. 2. 3. Find the circumference of a circle with diameter of 20 feet. Use 3.14 for . C = 25.12 in. Insert Lesson Title Here C = 18.84 in. 8 in. 62.8 ft 3 in. Course 1 9-8 Circles and Circumference

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