Investigating Circles

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


• C = x d

• C = 3.14 x 1.5

• C = 4.71cm

If the diameter is

1.5cm

EstimateIs . . .


• 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


• 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?

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

Investigating Circles

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