1. Investigating Circles

2. Properties of Circles

4. • Circle  radius diameter A closed curved with all points the same
distance from
center • 
origin
area
circumference

5. Origin The origin is the center of the circle. origin
All points on a circle are the same distance from the origin.
A circle is named by its center.
Name: Circle A
origin A

6. Diameter
The diameter is the distance of a line segment going across a circle through its center. AB
It divides the circle exactly in half.
Is viewed as a line of symmetry.
Symbol is lower case d.
diameter

7. Radius
Radius is the distance from the center of the circle to any point on the circle.
Radius is one-half the length of the diameter.
Symbol is lower case r.

8. Circumference
Circumference refers to the total distance around the outside of a circle.
Can also be called the perimeter of a circle.
Symbol is an upper case C.

9. Diameter, Radius, Circumference of a Circle

10. Diameter, Radius, Circumference of a Circle

11. Making Connections
You can estimate the age of a tree by measuring the circumference of a tree. For many kinds of trees, each 2 cm represents one year of growth.
100 cm

12. Making Connections
An odometer is an instrument used to measure the distance a vehicle travels by counting the number of wheel revolutions.

13. Properties of a Circle – Internet Activity SITE: www. harcourtschool
Properties of a Circle – Internet Activity SITE: SELECT: Math / Grade 7 / Glossary
For each word given, write a definition and illustrate an example.
Record work neatly and space between each definition.
title and date your page
Subtitle – Properties of a Circle (underline)
When you finish, go to site
Select Games, then the
1st Geometry Version
of Non-Java Games.
Words to Define
circle, circumference, diameter, radius
Tools Required
pencil, eraser, ruler, red pen, disc, looseleaf

14. Circle Properties closed curved
all points same distance from centre (origin)
radius
diameter
circumference
area pi

15. Concepts you Should Now Know
Origin
Diameter
Radius
Circumference
Ratio of C & d
center of a circle
distance across center of circle (d)
half the distance of diameter (r)
distance around the outside of a circle ( C )
Circumference is actually ( )
bigger than the diameter or about 3 times bigger

16. Diameter, Radius, Circumference of a Circle

17. Ratio Of The Circumference Of A Circle To Its Diameter
If you measure the distance around a circle (C) and divide it by the distance across the circle through its center (d), you should always come close to a particular value
We use the Greek letter  to represent this value.
 (pi)

18. Ratio Of The Circumference Of A Circle To Its Diameter
The value of  is approximately
So, C/d always = ___
Using  is a quicker way to find the circumference of a circle.
Using  allow us to calculate circumference with less measuring,
 (pi)

19. How  Helps
Knowing the value of ,allows us to use formulas to calculate circumference.
If the diameter of a circle is 2 cm, how could you calculate the circumference?
C =  x ___
Estimate the circumference
The circumference is ____
2cm

20. Circumference of a Circle
C = x d
C = 3.14 x 3
C = 9.42cm
If the
diameter is 3cm

21. Circumference of a Circle
Estimate
Is . . . 
C = x d
C = 3.14 x 1.5
C = 4.71cm
If the
diameter is 1.5cm

22. Circumference of a Circle
C =  x d
…but we don’t know the diameter 
C = x d
d = 2 x r
d = 2 x 3
d = 6
C = 3.14 x 6
C = 18.84m
If the
radius is 3m

23. Circumference of a Circle
C = x d
C = 3.14 x 5
C = 15.7
Estimate is . .
If the
diameter is 5

24. What formula could I use? What is the diameter of a circle if the
circumference
is 18.8?

25. What is the diameter of a circle if the
circumference
is 13.2?

26. What is the diameter of a circle if the
circumference
is 33.9?

27. Area of a Circle

28. Estimate the area of this circle.
Area of a Circle
Estimate the area of this circle.

29. Area of a Circle Seeing the square units can help.
Remember each block is one square unit
Estimate is

30. Area of a Circle
Counting square units can give you a good estimate, however, can be time consuming.
Counting will not always give an exact answer.
Actual is
The formula for finding the area of a circle is
A =  x r x r
or  r2
Estimate is

31. Pie are square? NO, pie are round!

32. Area of a Circle Estimated area is Remember A =  x r x r or  r2
Actual area is