Transcript Slide 1
10-2 Circles and Circumference 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 Holt CA Course 1 10-2 Circles and Circumference Vocabulary circle center radius (radii) diameter circumference pi Holt CA Course 1 10-2 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 Holt CA Course 1 10-2 Circles and Circumference Radius (plural: radii) A line segment with one endpoint at the center of the circle and the other endpoint on the circle. Radius Holt CA Course 1 Center 10-2 Circles and Circumference 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 Holt CA Course 1 10-2 Circles and Circumference Circumference The distance around a circle. Circumference Radius Center Diameter Holt CA Course 1 10-2 Circles and Circumference 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. Holt CA Course 1 10-2 Circles and Circumference Check It Out! Example 1 Name the circle, a diameter, and three radii. I D G H The center is point D, so this is circle D. IG is a diameter. DI, DG, and DH are radii. Holt CA Course 1 10-2 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 p, which is read “pi.” The decimal representation of pi starts with 3.14159265 . . . and goes on forever without repeating. Most people approximate p using 22 either 3.14 or . 7 Holt CA Course 1 10-2 Circles and Circumference C = p , you can Because d multiply both sides of the equation by d to get a formula for circumference. You can also substitute 2r for d because d = 2r. Holt CA Course 1 C =p d C d ·d=p·d C = pd C = p(2r) = 2pr 10-2 Circles and Circumference 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 = ? C = pd C 3.14 Write the formula. • 11 C 34.54 ft Holt CA Course 1 11 ft Replace p with 3.14 and d with 11. 10-2 Circles and Circumference 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 = ? C = 2pr C2 • 3.14 Write the formula. • C 31.40 cm Holt CA Course 1 5 cm 5 Replace p with 3.14 and r with 5. 10-2 Circles and Circumference 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 = pd C 3.14 Write the formula. • 9 C 28.26 ft Holt CA Course 1 Replace p with 3.14 and d with 9. 10-2 Circles and Circumference 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 = 2pr C2 • Write the formula. 3.14 • C 37.68 cm Holt CA Course 1 6 Replace p with 3.14 and r with 6. 10-2 Circles and Circumference 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 = pd 18.84 3.14d 18.84 _______ 3.14 3.14d _______ 3.14 6.00 cm d Holt CA Course 1 Write the formula. Replace C with 18.84 and p with 3.14. Divide both sides by 3.14.