Properties of a_circle
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Transcript of Properties of a_circle
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