bell work: solve: 3 x = 1 3 x = 1 5 4 5 4. answer: x = 5/12
TRANSCRIPT
Bell Work:
Solve:
3 x = 1
5 4
Answer:
x = 5/12
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
These are 2 commonly used formulas for the circumference of a circle.
c = πd c = 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 ≈ 3.14 π ≈ 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
12π 12 3
Practice:
What effect does doubling the diameter of a circle have on the circumference?
Answer:
Doubling the diameter doubles the circumference.
Diameter Circumference
6 6π12 12π24 24π
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.
Answer:
75(3.14)
≈ 236 meters
Practice:
The diameter of a circle on the playground is 12 feet. What is the radius of the circle?
Answer:
Radius = 6 feet
Practice:
A spoke on a bike wheel is about 12 inches long. The diameter of the wheel is about how many inches?
Answer:
24 inches
HW: Lesson 39 #1-30