10 1 Circles and Circumference 10 1 Circles

10 -1 Circles and Circumference A circle is the set of all points in

10 -1 Circles and Circumference A line segment with one endpoint at the center

10 -1 Circles and Circumference A diameter is a line segment that passes through

10 -1 Circles and Circumference Additional Example 1: Naming Parts of a Circle Name

10 -1 Circles and Circumference Check It Out: Example 1 Name the circle, a

10 -1 Circles and Circumference The distance around a circle is called the circumference.

10 -1 Circles and Circumference The ratio of the circumference to the diameter, C

10 -1 Circles and Circumference The decimal representation of pi starts with 3. 14159265.

10 -1 Circles and Circumference Additional Example 2: Application A skydiver is laying out

10 -1 Circles and Circumference Check It Out: Example 2 A second skydiver is

10 -1 Circles and Circumference Additional Example 3 A: Using the Formula for the

10 -1 Circles and Circumference Additional Example 3 B: Using the Formula for the

10 -1 Circles and Circumference Additional Example 3 C: Using the Formula for the

10 -1 Circles and Circumference Check It Out: Example 3 A Find the missing

10 -1 Circles and Circumference Check It Out: Example 3 B Find each missing

10 -1 Circles and Circumference Check It Out: Example 3 C Find each missing

10 -1 Circles Insert Lesson and Circumference Title Here Lesson Quiz Find the circumference

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10 -1 Circles and Circumference

10 -1 Circles and Circumference A circle is the set of all points in a plane that are the same distance from a given point, called the center. Center

10 -1 Circles and Circumference A line segment with one endpoint at the center of the circle and the other endpoint on the circle is a radius (plural: radii). Radius Course 1 Center

10 -1 Circles and Circumference 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. Radius Center Diameter Course 1

10 -1 Circles and Circumference Additional Example 1: Naming Parts of a Circle Name the circle, a diameter, and three radii. L Z M N The circle is circle Z. LM is a diameter. ZL, ZM, and ZN are radii. Course 1

10 -1 Circles and Circumference Check It Out: Example 1 Name the circle, a diameter, and three radii. I D G H The circle is circle D. IG is a diameter. DI, DG, and DH are radii. Course 1

10 -1 Circles and Circumference The distance around a circle is called the circumference. Circumference Radius Center Diameter Course 1

10 -1 Circles and Circumference The ratio of the circumference to the diameter, C , is the same for any circle. This d ratio is represented by the Greek letter , which is read “pi. ” C = d Course 1

10 -1 Circles and Circumference The decimal representation of pi starts with 3. 14159265. . . and goes on forever without repeating. We estimate pi using either 3. 14 22 or 7. The formula for the circumference of a circle is C = d, or C = 2 r. Course 1

10 -1 Circles and Circumference Additional Example 2: Application A skydiver is laying out a circular target for his next jump. Estimate the circumference of the target by rounding p to 3. C = d C 3 • 8 C 24 ft Course 1 t 8 f Write the formula. Replace with 3 and with 8. d

10 -1 Circles and Circumference 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. yd C = d Write the formula. 4 1 C 3 • 14 C 42 yd Course 1 Replace with 3 and d with 14.

10 -1 Circles and Circumference Additional Example 3 A: 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 = d C 3. 14 Write the formula. • 11 C 34. 54 ft Course 1 11 ft Replace with 3. 14 and d with 11.

10 -1 Circles and Circumference Additional Example 3 B: 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 = ? 5 cm C = 2 r C 2 • 3. 14 C 31. 4 cm Course 1 Write the formula. • 5 Replace with 3. 14 and r with 5.

10 -1 Circles and Circumference Additional Example 3 C: 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. 14 d Replace C with 21. 98 and with 3. 14. 21. 98 3. 14 d _______ 3. 14 Divide both sides by 3. 14. 7. 00 cm d Course 1 Write the formula.

10 -1 Circles and Circumference Check It Out: Example 3 A Find the missing value to the nearest hundredth. Use 3. 14 for pi. d = 9 ft; C = ? 9 ft C = d C 3. 14 Write the formula. • 9 C 28. 26 ft Course 1 Replace with 3. 14 and d with 9.

10 -1 Circles and Circumference Check It Out: Example 3 B Find each missing value to the nearest hundredth. Use 3. 14 for pi. r = 6 cm; C = ? 6 cm C = 2 r C 2 • Write the formula. 3. 14 • C 37. 68 cm Course 1 6 Replace with 3. 14 and r with 6.

10 -1 Circles and Circumference Check It Out: Example 3 C Find each missing value to the nearest hundredth. Use 3. 14 for pi. C = 18. 84 cm; d = ? C = d 18. 84 3. 14 d Replace C with 18. 84 and with 3. 14. 18. 84 3. 14 d _______ 3. 14 Divide both sides by 3. 14. 6. 00 cm d Course 1 Write the formula.

10 -1 Circles Insert Lesson and Circumference Title Here Lesson Quiz Find the circumference of each circle. Use 3. 14 for . 1. 2. 8 in. C = 25. 12 in. 3 in. C = 18. 84 in. 3. Find the circumference of a circle with diameter of 20 feet. Use 3. 14 for . 62. 8 ft Course 1