# Properties of a Circ

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```					                              radius
diameter

Circle
A closed curved
with all points
                 •
the same                 origin
distance from
center

area
circumference
Origin
• The origin is the
center of the           origin
circle.
• All points on a
circle are the same     A
distance from the
origin.
• A circle is named
by its center.
• Name: Circle A
Diameter
• The diameter is the
distance of a line
segment going across a    diameter

circle through its
center. AB
• It divides the circle
exactly in half.
• Is viewed as a line of
symmetry.
• Symbol is lower case d.
from the center of the
circle to any point on
the circle.
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         100
cm
circumference of a
tree. For many
kinds of trees,
each 2 cm
represents one
year of growth.
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.com
SELECT:      Math / Grade 7 / Glossary
• For each word given,
write a definition and           Words to Define
illustrate an example.          circle, circumference,
• Record work neatly and             diameter, radius
space between each
definition.
• title and date your page           Tools Required
• Subtitle – Properties of a      pencil, eraser, ruler, red
Circle (underline)                pen, disc, looseleaf
• When you finish, go to
site www.aplusmath.com
• Select Games, then the
1st Geometry Version
of Non-Java Games.
Concept Development
Activity 1
a)  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 2
a)   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 3
a) 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,
• 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.
Circumfer-
Group #   Object #    ence (C)
Diameter   C/d
(d)
Circle Properties
• closed curved
• all points same
distance from
centre (origin)
• diameter
• circumference
• area
• pi
Concepts you Should Now
Know
Origin           • center of a circle

Diameter         • distance across center of circle (d)

Radius           • half the distance of diameter (r)

• distance around the outside of a
Circumference   circle ( C )

Ratio of C & d

• 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              (pi)
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.
Ratio Of The Circumference
Of A Circle To Its Diameter
•   The value of  is
approximately
3.14159265358979323. . .
   (pi)
• 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,
How       Helps
• Knowing the value of ,allows us to
use formulas to calculate
2cm
circumference.
• If the diameter of a circle is 2 cm,
how could you calculate the
circumference?

• C =  x ___
• Estimate the circumference
• The circumference is ____
Circumference of a Circle
• C= x d

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

• C = 3.14 x 1.5
If the
diameter is
• C = 4.71cm                     1.5cm
Circumference of a Circle
C =  x d
•   C = x d         …but we
don’t know
•   d =2xr         the diameter
•   d =2x3
•   d =6                       If the
•   C = 3.14 x 6
•   C = 18.84m
Circumference of a Circle
• C= xd
Estimate
• C = 3.14 x 5     is . .

If the
diameter is 5
• C = 15.7
Diameter of a Circle
What formula
could I use?

What is the diameter
of a circle if the
circumference
is 18.8?
Diameter of a Circle

What is the diameter
of a circle if the
circumference
is 13.2?
Diameter of a Circle

What is the diameter
of a circle if the
circumference
is 33.9?
Estimate
the area of
this circle.
Seeing the
square units
can help.

Remember
each block
is one
Estimate is     square
unit
Counting will    Counting square
not always give    units can give
an exact
you a good
estimate,
however, can be
Actual
is                       time consuming.

The formula for
finding the area
of a circle is

Estimate is            A =  xrxr
or  r2
Pie are
square?
NO, pie are
round!
Remember   Estimate
d area is
A =xrxr
or  r
2

Actual
area is
Estimated
area is

Actual
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.com
Under lessons choose Circumference & Area of a Circle

• Read the site information.               Symbols are not
• Read, review, understand the              always is lower
examples.                                 case. R and D
• Read directions for the questions.
• Do the questions until correct.
• Check with me.                            Units of measure
are not metric.
• Repeat steps above, using:               Miles (mi) instead
- Area of a Circle                   of kilometers (km)
- Challenge
You Need:
Pencil, paper,calculator
Site:
www.mathgoodies.com/lessons/vol2/circumference.html

Symbols are not
always is lower
• Read the site information          case. R and D
the examples
questions                            Units of measure
• Do the questions until                are not metric.
correct.                            of kilometers (km)

You Need:
Pencil, paper,calculator
Site: www.mathgoodies.com
Choose Challenge Exercise: Read Directions Carefully
•   This activity is to be completed with a partner.
•   Read the site directions carefully.                         FORMULAS
•   You DO NOT need to copy questions or show your
work.
•   With your partner you are attempting to answer as            C =  x d
many of the challenge questions as possible.                 d = r x 2
Remember, get a mental picture, decide what is               r = d – 2
A =  x r x r
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     You Need: Pencil,
competition.
paper, calculator.
•   Have fun, but remember the guidelines.

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