CIRCLES AND CIRCUMFERENCE

CONTINUATION OF PI DAY In every circle, the ratio of the circumference to the diameter is equal to …… The Greek letter π (pi) stands for this number. And as you have already learned π=C/d or C=πd.

HERE ARE SOME KEY TERMS 1. Circle -is the set of all points in a plane that are the same distance from a given point in the plane. 2. Center- is the point given within the circle. 3. Diameter- is the distance across the circle through the center. 4. Radius- is the distance from the center to any point on the circle. 5. Chord- is the distance between any two points on the circle. 6. Circumference- is the distance around the circle.

FIGURE OF THE KEY TERMS

FORMULA FOR FINDING CIRCUMFERENCE OF A CIRCLE The circumference, denoted by C, of a circle is equal to its diameter times π, or 2 times its radius times π. Formula: C=πd (where d is the diameter) or C=2πr (where r is the radius)

EXAMPLE 1 Finding the Circumference of a Circle using the diameter. Round your answer to the nearest tenth.

WORK TO EXAMPLE 1 C=πd =π(18 in.) =18π inches =56.5 inches

EXAMPLE 2 Finding the Circumference of a Circle using the radius. Round your answer to the nearest tenth.

WORK TO EXAMPLE 2 C=2πr =2π(14 m.) =28π meters =88.0 meters

EXAMPLE 3 Compare the Circumference of Two Circles. Circle A Circle B

WORK TO EXAMPLE 3 Circumference of Circle A = πd = π(12 inches) = 37.7 inches Circumference of Circle B = πd = π(9 inches) = 28.3 inches Circumference of Circle B divided by the Circumference gives you that Circle B is ¾ the size of Circle A.

EXAMPLE 4 Sammy likes running and does most of his running in a circle. The circle is 400 meters around. He wants to know what is the distance between two points on the circle. Also, he wants to know the half distance. Can you help him?

WORK TO EXAMPLE 4 1. C=πd 400 meters =πd (400 meters)/π=d d=127.3 meters 2. C=2πr 400 meters=2πr (400 meters)/2π=r r=63.7 meters

PRACTICE PROBLEMS Page #2-44 EVEN