investigating circles
DESCRIPTION
Investigating Circles. Properties of Circles. radius. diameter. Circle A closed curved with all points the same distance from center. •. . origin. area. circumference. Origin. The origin is the center of the circle. - PowerPoint PPT PresentationTRANSCRIPT
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Circle A closed curved with all points
the same distance from
center
diameter
origin
circumference
radius
area
•
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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
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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
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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.
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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.
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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
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Making Connections
• An odometer is an instrument used to measure the distance a vehicle travels by counting the number of wheel revolutions.
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Circle Properties
• closed curved• all points same
distance from centre (origin)
• radius• diameter• circumference• area• pi
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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
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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)
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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)
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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
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Circumference of a Circle
• C = x d
• C = 3.14 x 3
• C = 9.42cm
If the diameter is
3cm
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Circumference of a Circle
• C = x d
• C = 3.14 x 1.5
• C = 4.71cm
If the diameter is
1.5cm
EstimateIs . . .
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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
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Circumference of a Circle
• C = x d
• C = 3.14 x 5
• C = 15.7
If the diameter is
5
Estimate is . .
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Diameter of a Circle
What is the diameter of a circle if the
circumferenceis 18.8?
What formula
could I use?
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Diameter of a Circle
What is the diameter of a circle if the
circumferenceis 13.2?
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Diameter of a Circle
What is the diameter of a circle if the
circumferenceis 33.9?
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Estimate the area of this circle.
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Seeing the square
units can help.
Remember each block is
one square
unit
Estimate is
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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
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Estimated area
is
Actual area is
Remember
A = x r x r
or r2
Remember
A = x r x r
or r2
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Actual area is
Estimated area
is
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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?
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Other skills
(2x – 5)(3x +6) FOIL
First
Outside
Inside
Last
Collect Like Terms
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Multiplying Binomials
(2x – 6)(x + 7)
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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
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Factoring
3x² + 12x + 12