Circle A closed curved with all points

the same distance from

center

diameter

origin

circumference

radius

area

•

Origin

• The origin is the center of the circle.

• All points on a circle are the same distance from the origin.

• A circle is named by its center.

• Name: Circle A

origin

A

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

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.

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.

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

Making Connections

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

Circle Properties

• closed curved• all points same

distance from centre (origin)

• radius• diameter• circumference• area• pi

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 3.14 ( )

bigger than the diameter or about 3 times bigger

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)

Ratio Of The Circumference Of A Circle

To Its Diameter• The value of is

approximately 3.14159265358979323. . .

• 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)

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

Circumference of a Circle

• C = x d

• C = 3.14 x 3

• C = 9.42cm

If the diameter is

3cm

Circumference of a Circle

• C = x d

• C = 3.14 x 1.5

• C = 4.71cm

If the diameter is

1.5cm

EstimateIs . . .

Circumference of a Circle

• 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

C = x d…but we

don’t know the

diameter

Circumference of a Circle

• C = x d

• C = 3.14 x 5

• C = 15.7

If the diameter is

5

Estimate is . .

Diameter of a Circle

What is the diameter of a circle if the

circumferenceis 18.8?

What formula

could I use?

Diameter of a Circle

What is the diameter of a circle if the

circumferenceis 13.2?

Diameter of a Circle

What is the diameter of a circle if the

circumferenceis 33.9?

Estimate the area of this circle.

Seeing the square

units can help.

Remember each block is

one square

unit

Estimate is

Estimate is

Counting square units

can give you a good estimate, however, can

be time consuming.

Counting square units

can give you a good estimate, however, can

be time consuming.

The formula for finding the

area of a circle is

A = x r x r

or r2

The formula for finding the

area of a circle is

A = x r x r

or r2

Counting will not always

give an exact answer.

Counting will not always

give an exact answer.

Actual is

Estimated area

is

Actual area is

Remember

A = x r x r

or r2

Remember

A = x r x r

or r2

Actual area is

Estimated area

is

Choosing a Formula

• To cut across a circular park has a you would travel 0.8 of a kilometer. How far would you travel around the park?

• A spoke of a bicycle wheel is 12 cm. What will be the distance of one turn of the wheel?

Other skills

(2x – 5)(3x +6) FOIL

First

Outside

Inside

Last

Collect Like Terms

Multiplying Binomials

(2x – 6)(x + 7)

Other SkillsFactoring

2x² + 14x + 12 Find a. b. c.

Multiply a x c

Find two numbers that add to b

( )( ) x in each

Divide by aKickback

Factoring

3x² + 12x + 12