Circumference of a Circles REVIEW. NAME MY PARTS Tangent – Line which intersects the circle at...
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Transcript of Circumference of a Circles REVIEW. NAME MY PARTS Tangent – Line which intersects the circle at...
Circumference of a Circles
REVIEW
NAME MY PARTS
Tangent
– Line which intersects the circle at exactly one point.
Point of Tangency
– the point where the tangent line and the circle intersect (C)
C
DL
M
Secant – Line which intersects the circle at exactly two points.e.g. DL
NAME EACH OF THE FOLLOWING:
EA
BD
C
O
1. A Circle
AnswerCircle O
NAME EACH OF THE FOLLOWING:
EA
BD
C
O
2. All radii
AnswerAO, BO, CO
DO, EO
NAME EACH OF THE FOLLOWING:
EA
BD
C
O
3. All Diameters
AnswerAD and BE,
NAME EACH OF THE FOLLOWING:
EA
BD
C
O
4. A secant
AnswerBC
k
NAME EACH OF THE FOLLOWING:
EA
BD
C
O
5. A Tangent
AnswerEK
k
NAME EACH OF THE FOLLOWING:
EA
BD
C
O
5. Point of Tangency
AnswerE
k
CIRCUMFERENCECircumference – is a distance around a circle.
Circumference of a Circle is determined by the length of a radius and the value of pi.
The formula is
C= 2r or C = d
r
P
EXAMPLE 1
WHAT IS THE CIRCUMFERENCE OF A CIRCLE IF RADIUS
IS 11 cm?
11 cm
R
Solution:C = 2r
C = 2( 11 cm)C = 22cm orC = 69.08 cm
EXAMPLE 2
THE CIRCUMFERENCE OF A CIRCLE IS 14cm. HOW
LONG IS THE RADIUS?
r=?
R
Solution:C = 2r
14cm = 2rDividing both sides by 2 .7 cm = r orr = 7 cm
AREA of a Circles
INVESTIGATION
IS IT POSSIBLE TO COMPLETELY FILLED THE CIRCLE WITH A SQUARE REGIONS?
R
NO.
INVESTIGATION
HOW IS THE AREA OF THE CIRCLE MEASURED?
R
In terms of its RADIUS.
INVESTIGATIONTAKE A CIRCULAR PIECE OF PAPER CUT INTO 16 EQUAL PIECES AND
REARRANGE THESE PIECES
WHAT IS THE NEW FIGURE
FORMED?r
NOTICE THAT THE NEW FIGURE FORMED
RESEMBLES A PARALLELOGRAM.
• 1
• 2
• 5 • 7 • 9• 11 • 13• 3
•8 • 10 • 12 • 14• 4 • 6
The BASE is approximately equal to half the circumference of the
circular region.
base = C orb= r
2
1
r h= r
Area of 14 pieces = area of the //gram = bh
= r( r) = r²
• 1
• 2
• 5 • 7 • 9• 11 • 13• 3
•8 • 10 • 12 • 14• 4 • 6
base = C orb= r
2
1
r h= r
EXAMPLE 1
WHAT IS THE AREA OF A CIRCLE IF radius
IS 11 cm?
11 cm
R
Solution:A = r ² = ( 11 cm)²A = 121cm² or = 379.94 cm²
EXAMPLE 2
WHAT IS THE AREA OF A CIRCLE IF radius
IS 4 cm?
4 cm
R
Solution:A = r ² = ( 4 cm)²A = 16cm² or = 50.24 cm²
EXAMPLE 3THE CIRCUMFERENCE OF A CIRCLE IS
14cm. WHAT IS THE AREA OF THE CIRCLE?
Solution:Step 1. find r.C = 2r
14cm = 2rDividing both sides by 2 .7 cm = r orr = 7 cm
Step 2. find the areaA = r ² = ( 7 cm)²A = 49cm² or = 153.86 cm²
EXAMPLE 4THE CIRCUMFERENCE OF A CIRCLE IS
10cm. WHAT IS THE AREA OF THE CIRCLE?
Solution:Step 1. find r.C = 2r
10cm = 2rDividing both sides by 2 .5 cm = r orr = 5 cm
Step 2. find the areaA = r ² = ( 5 cm)²A = 25cm² or = 78.5 cm²
TRUE OR FALSE
• 1. All radii of a circle are congruent.
• ANSWER TRUE
TRUE OR FALSE
• 2. All radii have the same measure.
• ANSWER FALSE
TRUE OR FALSE
• 3. A secant contains a chord.
• ANSWER TRUE
TRUE OR FALSE
• 4. A chord is not a diameter.
• ANSWER TRUE
TRUE OR FALSE
• 5. A diameter is a chord.
• ANSWER TRUE
AREAS OF REGULAR
POLYGONS
REGULAR POLYGONS3 SIDES 4 SIDES 5 SIDES 6 SIDES
7 SIDES 8 SIDES 9 SIDES 10 SIDES
Given any circle, you can inscribed in it a regular polygon
of any number of sides.
It is also true that if you are given any regular polygon, you can circumscribe a circle about it.
This relationship between circles and regular polygons leads us to
the following definitions.
The center of a regular polygon is the center of the circumscribed
circle.
The radius of a regular polygon is the distance from the center to
the vertex.
The central angle of a regular polygon is an angle formed by
two radii.
12
The apothem of a regular polygon is the (perpendicular) distance from the center of the
polygon to a side.
APOTHEM( a)
NAME THE PARTS
12
THE CENTERTHE RADIUSCENTRAL
ANGLE
ANGLE 1 AND ANGLE 2
NAME THE PARTS
APOTHEM
AREAS OF REGULAR POLYGONS
The area of a regular polygon is equal to HALF the product of the APOTHEM and the PERIMETER.
A = ½ap where, a is the apothem and p is the
perimeter of a regular polygon.
FIND THE AREA OF A REGULAR HEXAGONS WITH A 9 cm
APOTHEM.
HINT:A radius of a
regular hexagon bisects the
vertex angle.
9 CM
REMEMBER:Each vertex angle regular hexagon is
equal to 120°. each vertex = S ÷ n
FIND THE AREA OF A REGULAR HEXAGONS WITH A 9 cm
APOTHEM.
3
9
SOLUTION:Use 30-60-90 ∆
½s = = 3
Multiply both sides by 2
S= 6
9 CM
60
½ s
3
3 So, perimeter is equals to 36 3
FIND THE AREA OF A REGULAR HEXAGONS WITH A 9 cm
APOTHEM.
SOLUTION:A = ½ap
= ½( 9cm)36 cm = ½( 324 cm² )
= 162 cm²
9 CM
60
½ s
33
So, perimeter is equals to 36 3
3
FIND THE AREA OF A REGULAR triangle with radius 4
4 CM60
½ s
3