Bell Work: Solve: 3 x = 1 3 x = 1 5 4 5 4. Answer: x = 5/12.

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Bell Work: Solve: 3 x = 1 3 x = 1 5 4 5 4

Lesson 39: Circumference of a Circle

To draw a circle we can use a compass, a tool with a pivot point and a drawing point. As we swing the compass around its pivot point the drawing point traces a circle. Every point on the circle is the same distance from the center.

Radius*: the distance from the center of a circle to a point on the circumference of a circle. Diameter*: the distance across a circle measured through its center.

Circumference*: the distance around a circle.

Circumference is the specific name for the perimeter of a circle. The distance around a circle is related to the distance across the circle. If we take lengths equal to the diameter and wrap them around a circle, we would find that it takes a little more than three diameter lengths to complete the circumference.

The circumference of a circle is about 3.14 or 3 1/7 diameters, but these numbers are approximations of a special constant. A circumference is exactly π (pi) diameters. Thus the ratio of the circumference to the diameter of a circle is π.

circumference = π diameter diameter These are 2 commonly used formulas for the circumference of a circle. c = πdc = 2πr

Multiplying by π involves approximation, because π I an irrational number. There is no decimal or fraction that exactly equals π. This book will use two commonly used approximations for π. π ≈ 3.14π ≈ 22/7

Example: The diameter of a truck wheel is 35 inches. About how far does the wheel roll in one turn? (use 22/7 for π).

Answer: C = πd C = 22/7 (35 inches) C ≈ 110 inches

Example: The fan belt on Fernando’s car wraps around two circular pulleys. One pully has a diameter of 8 cm. the other has a diameter of 12 cm. what is the ratio of the pullys’ circumference?

Answer: 8π = 8 = 2 8π = 8 = 2 12π 12 3

Practice: What effect does doubling the diameter of a circle have on the circumference?

Answer: Doubling the diameter doubles the circumference. DiameterCircumference 66π 1212π 2424π

Practice: George Ferris designed a Ferris Wheel for the 1893 World Columbian Exposition in Chicago. The wheel was 75 meters in diameter. Calculate the circumference of the wheel to the nearest meter.

Practice: The diameter of a circle on the playground is 12 feet. What is the radius of the circle?

Practice: A spoke on a bike wheel is about 12 inches long. The diameter of the wheel is about how many inches?