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Circumference of a Circle

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Circumference of a Circle

Lesson 10.8

- the perimeter is the distance around a figure

6 units

6 units

6 units

6 units

Total Perimeter =

6 x 4 or 24 units.

11 units

3 units

Why is the perimeter/side ratio always 4?

A square consists of 4 sides of equal length. Therefore, the perimeter of a square is 4 times the length of one of its sides.

- Complete page 370 with a partner that does not sit at your table.
- You will need to take you time to understand what the question is asking.
- Read the question 1 carefully.
- Study the chart to understand the information it presents.
- Answer questions 2 & 3

- Today we are going to explore similar ratios for circles.
- What is the name for the perimeter of a circle?
- circumference

- What is the circumference of the Earth?

Vocabulary Time!!!!!

Take out your spiral!

radius

diameter

c

i

r

e

c

c

u

m

n

e

f

e

r

3 inches

6 inches

12 inches

24 inches

1.5 inches

3 inches

50 inches

100 inches

The radius is ½ of the diameter.

The diameter is twice the radius.

1 foot

1 foot

1 foot

1 foot

- You and a new partner will complete MJ page 371.
- Choose an object from the back table. (It doesn't have to be your object)
- Measure the circumference by wrapping the string around the widest part of the circle – make sure the string is straight around the object, not on an angle.

- Carefully remove the string from the object marking the starting and ending point of the circumference.
- Measure this length of string in centimeters using your ruler.
- Convert to millimeters. (÷10)
27 cm = 2.7 mm

- Record the length in millimeters.

- To determine diameter of spheres, place your object on the corner of a piece of computer paper.

- The points where the sides of the angle intersect the circle are the endpoints of the diameter.

- Complete the table
- When you record your answers, round to the hundredths place
- Answer question 5
- When you complete question 5, come to the board and input your information on the stem and leaf plot
- We will be working together to answer question 6

- Remember the perimeter/side ratio for a square?
- 4
- The circumference/diameter ratio also appears to be a constant with a value of between 3.1and 3.2
- The exact value of this ratio is an irrational number named for a letter of the Greek alphabet –π (pi)

circumference = π

diameter

- It is impossible to calculate the exact value of π
- In 1949, it was calculated out to 37,000 decimal places on one of the first computers
- In 1981 to 2 million digits on a supercomputer
- In 1999, there were more than 206 billion digits

- Because π goes on forever without a pattern, we use an approximation of its exact value.
- Because we approximate the value, our calculations of π cannot be exact.
- We will use the symbol ≈ to mean approximately equal to

- Return to the chart on MJ page 371
- Using the diameter measurement and the value of π, recalculate the circumference of one or two of your objects
- Remember your answer will be an estimate and will not be exact.