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### Circumference of a Circle

Lesson 10.8

Perimeter

- the perimeter is the distance around a figure

Find the perimeter to side ratio

11 units

Find the perimeter to side ratio

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.

Open Your Math Journals

- 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

Now How About Circles?

- 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?

We can conclude that the circumference is more than 2 diameters, but less than 4 diameters.

1 foot

Time to measure!

- 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.

Time to measure!

- 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.

Time to measure!

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

Time to measure!

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

Math Journal page 371

- 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

Results

- 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)

What is π ?

- 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

What is π ?

- 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

Let’s Practice

- 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.

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