Preview Warm Up California Standards Lesson Presentation

Warm Up The length and width of a rectangle are each multiplied by 5. Find how the perimeter of the rectangle changes. The perimeter is multiplied by 5.

California Standards MG1.1 Understand the concept of a constant such as p; know the formulas for the circumference and area of a circle. Also covered: AF1.1, AF3.1, AF3.2, MG1.2

Vocabulary circle center radius (radii) diameter circumference pi

A circle is the set of all points in a plane that are the same distance from a given point, called the center. Center

Radius (plural: radii) A line segment with one endpoint at the center of the circle and the other endpoint on the circle. Radius Center

Diameter A line segment that passes through the center of the circle and has both endpoints on the circle. Notice that the length of the diameter is twice the length of the radius, d = 2r. Radius Center Diameter

Circumference The distance around a circle. Radius Center Diameter

Additional Example 1: Naming Parts of a Circle Name the circle, a diameter, and three radii. L Z M N The center is point Z, so this is circle Z. LM is a diameter. ZL, ZM, and ZN are radii.

Name the circle, a diameter, and three radii. Check It Out! Example 1 Name the circle, a diameter, and three radii. G H D I The center is point D, so this is circle D. IG is a diameter. DI, DG, and DH are radii.

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 The decimal representation of pi starts with 3.14159265 . . . and goes on forever without repeating. Most people approximate p using either 3.14 or . 22 7

Because , you can multiply both sides of the equation by d to get a formula for circumference. You can also substitute 2r for d because d = 2r. C d =  C d =  C d · d =  · d C = d C = (2r) = 2pr

Additional Example 2: Application A skydiver is laying out a circular target for his next jump. Estimate the circumference of the target by using as an estimate for p. 22 7 10.5 ft C = d Use the formula. 22 7 C  • 10.5 22 7 Replace  with and d with 10.5. C  33 ft The circumference of the target is about 33 feet.

chalk design by using as an estimate for p. Check It Out! Example 2 A concrete chalk artist is drawing a circular design. Estimate the circumference of the chalk design by using as an estimate for p. 22 7 14 in. C = d Use the formula. 2 22 7 C  • 14 22 7 Replace  with and d with 14. 1 C ≈ 44 in. The circumference of the chalk design is about 44 inches.

Use as an estimate for  when the diameter or radius is a multiple of 7. 22 7 Helpful Hint

Additional Example 3: Using the Formula for the Circumference of a Circle A. Find the missing value to the nearest hundredth. Use 3.14 as an estimate for p. d = 11 ft; C = ? 11 ft C = d Write the formula. C  3.14 • 11 Replace  with 3.14 and d with 11. C  34.54 ft

Additional Example 3: Using the Formula for the Circumference of a Circle B. Find each missing value to the nearest hundredth. Use 3.14 as an estimate for p. r = 5 cm; C = ? 5 cm C = 2r Write the formula. C  2 • 3.14 • 5 Replace  with 3.14 and r with 5. C  31.40 cm

Check It Out! Example 3 A. Find the missing value to the nearest hundredth. Use 3.14 as an estimate for p. d = 9 ft; C = ? 9 ft C = d Write the formula. C  3.14 • 9 Replace  with 3.14 and d with 9. C  28.26 ft

Check It Out! Example 3 B. Find each missing value to the nearest hundredth. Use 3.14 as an estimate for p. r = 6 cm; C = ? 6 cm C = 2r Write the formula. C  2 • 3.14 • 6 Replace  with 3.14 and r with 6. C  37.68 cm

Replace C with 18.84 and  with 3.14. Check It Out! Example 3 C. Find each missing value to the nearest hundredth. Use 3.14 as an estimate for p. C = 18.84 cm; d = ? C = d Write the formula. 18.84  3.14d Replace C with 18.84 and  with 3.14. 18.84 3.14d _______ 3.14 3.14  Divide both sides by 3.14. 6.00 cm  d

Lesson Quiz Find the circumference of each circle. Use 3.14 as an estimate for . 1. 2. 3. Find the circumference of a circle with diameter of 20 feet. Use 3.14 as an estimate t for . C ≈ 25.12 in. C ≈ 18.84 in. C ≈ 62.8 ft