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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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Presentation Transcript
  • 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 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?

Vocabulary Time!!!!!

Take out your spiral!

add this diagram to your notes
Add this diagram to your notes
















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.

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
  • 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


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.