circumference of a circle lesson 10.8. perimeter the perimeter is the distance around a figure
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Find the perimeter to side Find the perimeter to side ratioratio
Total Perimeter =6 x 4 or 24 units.
Side Perimeter Perimeter/Side
6 units 24 24/6= 4 units
Find the perimeter to side Find the perimeter to side ratioratio
11 units
Side Perimeter Perimeter/Side
11 units 44 44/11=4
Find the perimeter to side Find the perimeter to side ratioratio
3 units
Side Perimeter Perimeter/Side
3 units 12 12/3=4
Find the perimeter to side Find the perimeter to side ratioratio
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?
Add this diagram to your Add this diagram to your notesnotes
diameter
radius
ci
r
cu m f e r e n c
e
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)
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