ARC LENGTH
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DEPARTMENT OF EDUCATIONDIVISION OF CITY SCHOOLS
ERNESTO RONDON HIGH SCHOOL
MATHEMATICSDEPARTMENT
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Featuring: CIRCLE
THE DOODLE GAME
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an unfocused drawing made while a person's attention is otherwise occupied. Doodles are simple
drawings that can have concrete representational meaning or may
just be abstract shapes.
*DOODLE
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GUESS MY FIGURE 543210
MEXICAN FRYING AN EGG
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A TAHO VENDOR
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AN ICE SCREAM VENDOR
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MEXICAN PLAYING A TRUMPET
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MEXICAN RIDING A BICYCLE
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MEXICAN TAKING A BATH
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MEXICAN COUPLE KISSING
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GIRAFFE PASSING BY THE WINDOW
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KOALA BEAR CLIMBING A TREE
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THREE MEXICANS PEEING
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RECALL
How do you call on the distance between the center and a point on the circle?
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RECALL
How do you call on the angle whose vertex is at the center and whose sides are the radii of the circle?
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RECALL
How do you call on a subset /any part of a circle.
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ARCARC
RADIUSCENTRAL ANGLECENTRAL ANGLE
RADIUS
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ARC LENGTH
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ARC LENGTHit refers to the fractional part of the circumference subtended by the arc in a circle. Radian
measure is used to find the arc length.
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GROUP ACTIVITY NO. 4
You are given 7 minutes to answer the activity. Speed and accuracy are
important.
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09000 7 87654321560 04 98765432103 9876543210987654321021 987654321098765432100Hours Minutes Seconds
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09000 6 87654321550 04 98765432103 9876543210987654321021 987654321098765432100Hours Minutes Seconds
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09000 5 87654321540 04 98765432103 9876543210987654321021 987654321098765432100Hours Minutes Seconds
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09000 4 87654321530 04 98765432103 9876543210987654321021 987654321098765432100Hours Minutes Seconds
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09000 3 87654321520 04 98765432103 9876543210987654321021 987654321098765432100Hours Minutes Seconds
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09000 2 87654321510 04 98765432103 9876543210987654321021 987654321098765432100Hours Minutes Seconds
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09000 1 87654321500 04 98765432103 9876543210987654321021 987654321098765432100Hours Minutes Seconds
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A
BC
D
E
FG
H
45°
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A
B
45°
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The arc length (s) is directly proportional to the radius (r) of the circle. While the central angle (Ѳ) is constant.
In equation:s /r = Ѳ
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where:s – arc length of the circler – radius of the circleѲ – central angle in
radian measure
s = Ѳ•r
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1. Find arc length (s) of the circle illustrated below.
SAMPLE EXERCISE
π/35cms
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π/35cm s SOLUTION:s = ѳ • r = π/3 • 5 = 5π/3
ANSWER: s = 5π/3 cm.
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2. Find arc length (s) of the circleSAMPLE EXERCISE
100°7cms
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SOLUTION:
s = ѳ • r = 5π/9 • 7 = 35π/9
ANSWER: s = 35π/9 cm.
100°7cms
Change the central angle to radian measure
100° x π/180 °5π/9
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3. The radius of the circle is 25mm. Find the length of an arc of the circle subtended by a central of 60°.
SAMPLE EXERCISE
SOLUTION:s = ѳ • r = π/3 • 25 = 25π/3mm
60° x π/180 °π/3
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SUMMING UP!
What have added inside the coconut shell?
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Quiz no. 5Find the arc length of a circle having the radius r and central angle with measure Ѳ.
1. r = 4 feet, Ѳ = π/42. r = 6inches, Ѳ = 330°3. r= 10meters , Ѳ = 150°
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ASSIGNMENT
3.82 m
R
Q
P
7.64 in.
18 in.
Z
Y
X
Find the circumference
Find the central angle
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Thank You