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.

Properties of a Circle – Internet Activity

SITE: www.harcourtschool.comSELECT: 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 www.aplusmath.com • Select Games, then the 1st Geometry Version of Non-Java Games.

Words to Definecircle, circumference,

diameter, radius

Words to Definecircle, circumference,

diameter, radius

Tools Requiredpencil, eraser, ruler, red

pen, disc, looseleaf

Tools Requiredpencil, eraser, ruler, red

pen, disc, looseleaf

Concept DevelopmentActivity 1a) With masking tape label the 4 circular shaped objects

1,2,3 and 4.b) Use the tape measure to find the circumference of each

object. Measure carefully! (Use cm)c) Record results in the chart provided as you measure

each object. Include unit of measure.

Activity 2a) Trace around each object and then cut your tracing

out. Trace and cut carefully! Label traced copy (object # ?) Also, put your names on the trace copy.

b) Fold each circle exactly in half and crease along the fold line.

c) Measure the diameter of each circle.

d) Record results in the chart provided. Check with me.

Concept Development(con’t)

Activity 3a) Using the calculator provided, divide each

objects circumference by its diameter.b) Record results to the nearest hundredths

in column C/d. Check results.c) Look carefully at your results and discuss

with your partner any similarities you notice. Think, and answer the question below chart.

d) Check with me.

Clean UP• Return circular objects to table• Calculators, scissors, tape and

measuring tapes back in envelope, return to front table.

• Staple circles together give to me.

• Turn chart in to me.• Pick up all small bits of paper

and put in trash.• Large pieces of paper to table.

Group # Object # Circumfer-ence (C)

Diameter (d)

C/d

         

         

         

         

         

         

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

Pie are square? NO, pie

are round!

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?

Site: www.mathgoodies.comUnder lessons choose Circumference & Area of a

Circle1st Start with Circumference of a Circle

• Read the site information.

• Read, review, understand the examples.

• Read directions for the questions.

• Do the questions until correct.

• Check with me.

• Repeat steps above, using:

- Area of a Circle

- Challenge

Symbols are not always is lower case. R and D

instead of r and d

Units of measure are not metric. Miles (mi) instead of

kilometers (km)

You Need:Pencil,

paper,calculator

Site: www.mathgoodies.com/lessons/vol2/circumference.ht

ml

• Read the site information• Read, review, understand

the examples• Read directions for the

questions• Do the questions until

correct.

Symbols are not always is lower case. R and D

instead of r and d

Units of measure are not metric. Miles (mi) instead of

kilometers (km)You Need:Pencil,

paper,calculator

Site: www.mathgoodies.comChoose Challenge Exercise: Read Directions Carefully

• This activity is to be completed with a partner.• Read the site directions carefully.• You DO NOT need to copy questions or show your

work.• With your partner you are attempting to answer as

many of the challenge questions as possible. Remember, get a mental picture, decide what is being asked, choose a formula or create your own, work it out. Scrap paper can be used.

• When you get a correct answer, number and record the answer on paper. This paper is to be turned in.

• If you are unable to get an answer you are allowed to skip a question. # each questions, put ? if skipped.

• DO NOT share information or communicate with other groups. Work using a quiet voice as this is a competition.

• Have fun, but remember the guidelines.

You Need: Pencil, paper,

calculator.

FORMULAS

C = x dd = r x 2r = d – 2

A = x r x r