Circumference of a Circle Lesson 10.8. Perimeter the perimeter is the distance around a figure.

Circumference of a CircleCircumference of a Circle

Lesson 10.8

PerimeterPerimeterthe perimeter is the distance

around a figure

Find the perimeter to side Find the perimeter to side ratioratio

6 units

6 units 6 units

6 units


Total Perimeter =6 x 4 or 24 units.

Side Perimeter Perimeter/Side

6 units 24 24/6= 4 units


11 units


11 units 44 44/11=4


3 units


3 units 12 12/3=4


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 JournalsComplete 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?

CircumferenceCircumference

Vocabulary Time!!!!!

Take out your spiral!

How about a tune?How about a tune?

Add this diagram to your Add this diagram to your notesnotes

diameter

radius

ci

r

cu m f e r e n c

e

What do you notice?What do you notice?

3 inches

6 inches


12 inches

24 inches


1.5 inches

3 inches


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 Is the circumference longer or shorter than the or shorter than the diameter?diameter?

1 foot

Is the circumference longer Is the circumference longer than twice the diameter?than twice the diameter?

1 foot

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

1 foot

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

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.

Time to measure!

Math Journal page 371Math Journal page 371Complete the tableWhen you record your answers,

round to the hundredths placeAnswer question 5When 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

ResultsResultsRemember the perimeter/side

ratio for a square?4The 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 circleRatio of a circle

circumference = πdiameter

Mathematical PiMathematical Pi

I love piI love pi

What is What is ππ ? ?It is impossible to calculate the

exact value of πIn 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 What is ππ ? ?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 PracticeLet’s PracticeReturn to the chart on MJ page

371Using 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.

Circumference of a Circle Lesson 10.8. Perimeter the perimeter is the distance around a figure.

Documents

Transcript of Circumference of a Circle Lesson 10.8. Perimeter the perimeter is the distance around a figure.