circles & circumference standard math this is a circle
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Circles & Circumference
Standard Math
This is a circle.
A circle
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Many musical instruments have a circular surface.
For example:
Bingo Drum Tabla
Snare Drum Bass DrumBACK
Five rings in the logo of Olympic gamesBACK
A circle
Radius
This is the radius of a circle. It is a line segment starting from the center of the circle.
The radius of this circle is four inches.
4 in.
Diameter
To find the length across the circle you would double the radius.
4 in.4 in
The line segment that forms across is called the diameter.
DIAMETER
4 in + 4 in = 8 in
Circumference
To find the measurement all around the circle you would multiply the diameter by 3.14 or 3 for a good estimate!!
Let’s Try!------------------->
Measuring Around the Circle
Remember the radius is 4 inches.Double it to find the diameter.
4 in +4 in =8 in
The best estimate of the length around the circle is 24 inches.8 in x 3 in = 24 in
4 in
8 inches
Measuring CirclesReview
Radius Diameter
CircumferenceMeasurement
ALL around the circle.
Find the diameter:
5 in. 3 in
7 in.
10 inches
6 inches
14 inches
Find the CircumferenceLength around the circle.
5 in. 3 in
7 in.
30 inches
18 inches
42 inches
. .
Circles
• A Circle is a set of points that are all the same distance from a given point, called the center or the origin. A circle is named by its origin.
• A radius of a circle is a line segment with one endpoint at the origin and the other endpoint on the circle.
Circles
• A chord is a line segment with both endpoints on the circle
• A diameter is a chord that passes through the origin of the circle.
ArcPart of a circle named by its endpoints
Radius
Line segment whose endpoints are the centerof a circle and any point on the circle
Diameter
Line segment that passesthrough the center of a circle, and whose endpoints lie on the circle
ChordLine segment whose endpoints are any twopoints on a circle
Radius Diameter Chord ArcSemiCircle
CentreO
Radius Diameter Chord ArcSemiCircle
Radius
OM
Centre
M
O
Radius Diameter Chord ArcSemiCircle
Centre
ED
Diameter DE
O
Radius Diameter Chord ArcSemiCircle
Centre
Chord PQ
P
Q
O
Radius Diameter Chord ArcSemiCircle
Centre
E
G
Arc PQR
O
F
Radius Diameter Chord ArcSemicircle
S
CentreO
Diameter
Semicircle
D E
Semicircle DSE
Semicircle
C2
C
UM
F
E
R
N
C
E
A
E
I
Down1. The distance between any two points on the circumference of the circle.2. The distance around the circle.
3. The distance from the centre of the circle to a point on the circle.
R
D
IU
S
R
1
C
3R
A
Across:4. The line segment that joins any
two points on the circle and passes through its centre.
5. A closed curve in a plane.6. All points on the circle are equidistant from this point.7. A line segment that joins any
two points on a circle.
4 D A M TE E
5 I R L E
6C E N T E
H RO D7
Name the parts of circle M.
Additional Example 1: Identifying Parts of Circles
O
N
P
Q
R
M
A. radii:
B. diameters:
C. chords:
MN, MR, MQ, MO
NR, QO
NR, QO, QN, NP
Radii is the plural form of radius.
Reading Math
Name the parts of circle M.
Check It Out! Example 1
A. radii:
B. diameters:
C. chords:
GB, GA, GF, GD
BF, AD
A
B
C
D
EF
G
H
AH, AB, CE,
BF, AD
The circumference is the distance around a circle.
Circumference
Circumference is the perimeter of circles.
Radius is half of the diameter.
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dCr C or 2
:is ceCircumfren find toformula The
7
22or 3.14
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Find the Circumference of the circle.
rC 2
214.32C
yd. 56.12CBACK
Find the circumference using the diameter.
π dC
1014.3C
in. 4.31C
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Find the circumference of the circle.
π dC
1614.3C
ft. 24.50C
You try this one.
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Area Of A Circle
A = πr²3.14 or ²²/₇
Example 1: A = π r²
A = 3.14 ( 4 )² A = 3.14 ( 16 ) A = 50.24 in²
4 in
Example 2:
A = πr²A = 3.14 ( 3 )²A = 3.14 ( 9 )A = 28.26 cm²
6 cm
Example 1: Find the area of this circle
25 cm
A = r2
= 252
= 196 cm2to 1 decimal place
Key into your calculator:
25 and then press the [x2] button
Example 2: Find the circumference of this circle
256 m
A = r2
= 1282
= 515 m2
to the nearest whole numberHere we know the diameter so we have to divide it by 2 to get the radius
Radius = 256 2 = 128 m
Circles & Circumference
Standard MathBACK