Transcript Areas of Circles, Sectors, and Segments

Adv Geo Starter
• Given: Circle B is congruent to Circle D
•
Arc AE is congruent to Arc CE
• Prove: ABCD is a parallelogram
A
B
•E
C
D
Circumference
and Arc Length
10.9
Definition of Circumference
• The circumference of a
circle is its perimeter.
Postulate
C  2r or d
Length of an Arc
 m arcPQ
lengthof arc PQ  
2r
 360 
OR
length of arc PQ
m arc PQ

2r
360
Example 1
Find the circumference of circle
O and the length of arc AB
8
O
A
45°
C = 16π
arc AB = 2π
B
Example 2
Find length of arc AB
Given: m arc AB = 60°
radius = 12 cm
Find: the length of arc AB
Areas of Circles, Sectors, and
Segments
Section 11.6
Review:
Find the area of the circle.
d = 16
64π
Review:
Find the radius of the circle.
A = 90π
3√10
Sector
• The region bounded by two
radii and an arc of the circle.
Sector
Theorem
Asec tor
measure of arc 2
(
)r
360
OR
Asec tor measure of arc

2
r
360
Segment of a circle
A region bounded by a chord of the
circle and its corresponding arc.
A(segment) = A(sector) – A(Δ)
Segment
Example 3
Find the area of a sector with
a radius of 9 and a 60° arc.
Area?
13.5π
Example 4
Find the area of the segment.
20
100π-200
Example 5
• The diameter of a bicycle wheel (including the tire) is
70 cm.
• A) How far will the bike travel if the wheel rotates
1000 times? (Approximate the answer in meters).
• Hint: Distance = (#of revolutions)(distance per
revolution)
• B) How many revolutions will the wheel make if the
bike travels 15 m? (Approximate to the nearest
tenth of a revolution)
Example 5 Solution
• A) Distance = (# of revol)(dist per revol)
•
≈ (1000)(220)
•
≈ 220000
• The bike will travel 220,000 cm or 2200m.
• B) The bike travels approximately 2.2 m per
revolution. Let x = # of revolutions.
• Distance = (# of revol)(dist per revol)
• 15 ≈ x (2.2)
• 6.8 ≈ x
•
The wheel will revolve ≈6.8 times.
Stations
• You will be assigned a partner and
3 problems.
• Each of you has to copy the
problem, show work, and turn in
your paper.
Homework
• p. 501 #3 – 8, 10
• p. 539 #5, 6, 9 - 11, 14
EXIT SLIP
• Explain how to find the area of a
segment of a circle.
• Draw a diagram to illustrate!