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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
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 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!

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.

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

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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