Circumference of a Circle

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# Circumference of a Circle - PowerPoint PPT Presentation

Circumference of a Circle. Lesson 10.8. Perimeter. the perimeter is the distance around a figure. Find the perimeter to side ratio. 6 units. 6 units. 6 units. 6 units. Find the perimeter to side ratio. Total Perimeter = 6 x 4 or 24 units. Find the perimeter to side ratio. 11 units.

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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

6 units

6 units

6 units

6 units

Find the perimeter to side ratio

Total Perimeter =

6 x 4 or 24 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.

• 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?
Circumference

Vocabulary Time!!!!!

diameter

c

i

r

e

c

c

u

m

n

e

f

e

r

What do you notice?

3 inches

6 inches

What do you notice?

12 inches

24 inches

What do you notice?

1.5 inches

3 inches

What do you notice?

50 inches

100 inches

So, what did you notice?

The radius is ½ of the diameter.

The diameter is twice the radius.

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 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)
Ratio of a circle

circumference = π

diameter

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