Circles: Formulas for Circumference, Area, and Proportions for Arc Length and Sector Area
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We will learn to…
•
Use
formulas to
find
circumference
&
area
of
circles.
Circle:
Area:
A =
r
2
NOTE:
Radius is half the diameter.
-- OR –
Diameter is double the radius.
Circumference:
C =
d
or
C = 2
r
• Distance around the edge of a circle
Formula:
• the size of a surface
Formula:
E
X
A
M
P
L
E
1
Use the formula for circumference
Round to the nearest hundredth if necessary.
=
2
π
(
9
)
=
1
8
π
≈ 56.55
a
.
F
i
n
d
t
h
e
c
i
r
c
u
m
f
e
r
e
n
c
e
o
f
a
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l
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w
i
t
h
a
r
a
d
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u
s
o
f
9
c
m
S
O
L
U
T
I
O
N
C
=
2
π
r
E
X
A
M
P
L
E
1
Use the formula for circumference
4.14 ≈ r
C
=
2
π
r
b
.
F
i
n
d
t
h
e
r
a
d
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o
f
2
6
m
S
O
L
U
T
I
O
N
Round to the nearest hundredth if necessary.
2
π
2
π
E
X
A
M
P
L
E
2
Use the formula for area of a circle
Round to the nearest hundredth if necessary.
SOLUTION
= π(2.5)
2
= 6.25π
≈ 19.63
A
= π
r
2
E
X
A
M
P
L
E
2
Use the formula for area of a circle
Round to the nearest hundredth if necessary.
113.1 = π
r
2
6 ≈
r
A
= π
r
2
SOLUTION
π
π
We will learn to…
•
Use
proportions
to
find
arc length
&
sector
area
of
circles
.
Arc:
part of the
circumference
Sector:
Part of area
(piece of circle)
Arc Length
Circumference
360°
=
Sector Area
Area of Circle
360°
=
Arc Length = (
θ
/360°) * 2
π
r
Sector Area = (
θ
/360°) *
π
r
2
E
X
A
M
P
L
E
3
Find arc lengths and related measures
Round to the nearest hundredth if necessary.
SOLUTION
Arc length ≈ 8.38 cm
360
x
= 3015.93
C = 2
(8)
≈ 50.27 cm
E
X
A
M
P
L
E
3
Find arc lengths and related measures
Round to the nearest hundredth if necessary.
SOLUTION
C
= 37.71 in.
40
C
= 1508.4
E
X
A
M
P
L
E
3
Find arc lengths and related measures
Round to the nearest hundredth if necessary.
SOLUTION
C = 2
(15.28)
≈ 96 m
m
RTS
= 165°
15840 = 96
x
E
X
A
M
P
L
E
4
Find sector areas and related measures
Round to nearest hundredth if necessary.
SOLUTION
A ≈ 39.10 units
2
A =
(8)²
≈ 201.06 units
360
A
= 14074.34
E
X
A
M
P
L
E
4
Find sector areas and related measures
Round to nearest hundredth if necessary.
SOLUTION
A
= 315 m
2
40
A
= 12600
You turn
Complete practice problems 1-8 on your handout
–
First five minutes on your own (in silence)
Answers to Practice
1.
C ≈ 15.71 in. 5. Area
≈ 615.75 ft.
2
2.
diameter
≈ 5.41 ft. 6. Area ≈ 205.25 ft.
2
3.
Arc length ≈ 5.89 yd 7. Area ≈ 410.50 ft.
2
4.
C = 81.68 m 8. Area = 907.92 cm
2
Arc:
part of the
circumference
Sector:
piece of the
circle
Arc Length
Circumference
360°
=
Sector Area
Area of Circle
360°
=
Learn how to calculate the circumference and area of circles using formulas, and use proportions to find arc length and sector area. Master the concepts through examples and practical applications in geometry.
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Presentation Transcript
12/5: Use formulas to find circumference & area of circles and use proportions to find arc length & sector area of circles. Do Now Agenda Homework Do Now! On your desk: - Pencil & Calculator Handout - Today s handouts Guided Practice (10 problems) Independent Practice Do Do Now! Exit Ticket
We will learn to Use formulas to find circumference & area of circles.
Circle: Circumference: Distance around the edge of a circle C = d or C = 2 r Formula: Area: the size of a surface NOTE: A = r2 Formula: Radius is half the diameter. -- OR Diameter is double the radius.
EXAMPLE 1 Use the formula for circumference Round to the nearest hundredth if necessary. a. Find the circumference of a circle with a radius of 9 cm SOLUTION C=2 r ANSWER 56.55 cm =2 (9) =18 56.55
EXAMPLE 1 Use the formula for circumference Round to the nearest hundredth if necessary. b. Find the radius of a circle with a circumference of 26 m SOLUTION ANSWER C =2 r 4.14 m 26 2 = 2 r 2 26 2 = r 13/ = r 4.14 r
EXAMPLE 2 Use the formula for area of a circle Round to the nearest hundredth if necessary. a. Find the area of the figure below if its radius is 2.5 cm SOLUTION ANSWER A = r2 19.63 cm2 = (2.5)2 = 6.25 19.63
EXAMPLE 2 Use the formula for area of a circle Round to the nearest hundredth if necessary. b. Find the diameter of the CD if its area is 113.1 cm2. SOLUTION ANSWER A = r2 d = 12 cm 113.1 = r2 113.1 = r2 = r2 36 6 r
We will learn to Use proportions to find arc length & sector area of circles.
Arc: part of the circumference Sector: Part of area (piece of circle) Arc Length Arc Length Sector Area = = 360 360 Circumference Area of Circle Sector Area = ( /360 ) * r2 Arc Length = ( /360 ) * 2 r
EXAMPLE 3 Find arc lengths and related measures Round to the nearest hundredth if necessary. a. Find the arc length of AB SOLUTION Arc Length = 360 Circumference C = 2 (8) 50.27 cm x 60 = 50.27 360 360x = 3015.93 Arc length 8.38 cm
EXAMPLE 3 Find arc lengths and related measures Round to the nearest hundredth if necessary. b. Find the circumference. SOLUTION Arc Length = 360 Circumference 40 4.19 C = 360 40C = 1508.4 C = 37.71 in.
EXAMPLE 3 Find arc lengths and related measures Round to the nearest hundredth if necessary. c. Find the m RTS. SOLUTION Arc Length = 360 Circumference C = 2 (15.28) 96 m 44 96 x = 360 15840 = 96x m RTS= 165
EXAMPLE 4 Find sector areas and related measures Round to nearest hundredth if necessary. a. Find the area of small sector SOLUTION Sector Area = 360 Area of Circle A = (8) 201.06 units A 70 360 = 201.06 360A = 14074.34 A 39.10 units2
EXAMPLE 4 Find sector areas and related measures Round to nearest hundredth if necessary. b. Find the area of circle SOLUTION Sector Area = 360 Area of Circle 40 35 A = 360 40A = 12600 A = 315 m2
You turn Complete practice problems 1-8 on your handout First five minutes on your own (in silence)
Answers to Practice 5. Area 615.75 ft.2 1. C 15.71 in. 2. diameter 5.41 ft. 6. Area 205.25 ft.2 3. Arc length 5.89 yd 7. Area 410.50 ft.2 4. C = 81.68 m 8. Area = 907.92 cm2
Arc: part of the circumference Sector: piece of the circle Arc Length Arc Length Sector Area = = 360 360 Circumference Area of Circle
