Circumference of a circle
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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. 11 units.

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Circumference of a Circle

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Circumference of a circle

Circumference of a Circle

Lesson 10.8


Perimeter

Perimeter

  • the perimeter is the distance around a figure


Find the perimeter to side ratio

Find the perimeter to side ratio

6 units

6 units

6 units

6 units


Find the perimeter to side ratio1

Find the perimeter to side ratio

Total Perimeter =

6 x 4 or 24 units.


Find the perimeter to side ratio2

Find the perimeter to side ratio

11 units


Find the perimeter to side ratio3

Find the perimeter to side ratio

3 units


Find the perimeter to side ratio4

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

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

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?


Circumference

Circumference

Vocabulary Time!!!!!

Take out your spiral!


How about a tune

How about a tune?


Add this diagram to your notes

Add this diagram to your notes

radius

diameter

c

i

r

e

c

c

u

m

n

e

f

e

r


What do you notice

What do you notice?

3 inches

6 inches


What do you notice1

What do you notice?

12 inches

24 inches


What do you notice2

What do you notice?

1.5 inches

3 inches


What do you notice3

What do you notice?

50 inches

100 inches


So what did you notice

So, what did you notice?

The radius is ½ of the diameter.

The diameter is twice the radius.


Is the circumference longer or shorter than the diameter

Is the circumference longer or shorter than the diameter?

1 foot


Is the circumference longer than twice the diameter

Is the circumference longer than twice the diameter?

1 foot


Which path is longer around the square or around the circle

Which path is longer-around the square or around the circle?

1 foot


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

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

1 foot


Time to measure

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 measure1

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 measure2

Time to measure!

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


Time to measure3

Time to measure!

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


Math journal page 371

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

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

Ratio of a circle

circumference = π

diameter


Mathematical pi

Mathematical Pi


I love pi

I love pi


What is

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 is1

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

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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