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Arc Length and
Area of a Sector
Arc length of a circle
Q. What is an arc ?
A
B
Answer
An arc is a fractionof the circumference.
minor arc
major arc
Arc length of a circle
Q. Find the circumference of the circle .
Solution
C D
3.14 20C
62.8C cm
10cm
Arc length of a circle
45 (3.14 12)
360
o
oarc length
length 4.71arc cm
Arc lengthπD
Central angle
360o=
Q. What is the length of the minor arc XY below ?
6 cm45
o
x
y
360o
connection
Arc length of a circle
60 (3.14 18)
360
o
oarc length
length 9.42arc cm
Arc lengthπD
Central angle
360o=
Q. What is the length of the minor arc AB below ?
9 cm
60o
A
B
connection
Arc length of a circle
260 (3.14 20)
360
o
oarc length
length 45.38arc cm
Arc lengthπD
Central angle
360o=
Q. What is the length of the major arc PQ below ?
10 m
100o
A
B
connection
260o
Area of Sector in a circle
A
B
minor sector
major sector
Area of Sector in a circle
Q. What is the area of the circle ?
Solution
2A r23.14 10A
2314A cm
10cm
Area of Sector in a circle
245Area of Sector (3.14 6 )
360
o
o
2Area Sector 14.14 cm
Area Sector
πr2
Central angle
360o=
What is the area of the minor sector XY below ?
6 cm45
o
x
y
360o
connection
Area of Sector in a circle
260Area Sector (3.14 9 )
360
o
o
2 Sector 42.41Area cm
Area Sector
πr2
Sector angle
360o=
Q. What is the area of the minor sector AB below ?
9 cm
60o
A
B
connection
Area of Sector in a circle
2260Sector Area (3.14 10 )
360
o
o
2Area Sector 226.89 cm
Sector Areaπr2
Central angle360o=
Q. What is the area of the major sector PQ below ?
10 m
100o
A
B
connection
260o
More examples…
Arc length of a circle
7.07360
(3.14 18)
o ox
45o ox
Arc lengthπD
Central angle360o
=
Q. The arc length is 7.07cm. Find the angle xo
9 cm
xo
A
B
connection
Area of Sector in a circle
o2
235.62x 360
(3.14 10 )
o
ox 270 o
Sector Areaπr2
Central angle
360o=
Q. Find the angle given area of sector AB is 235.62cm2 ?
10 m
A
B
connection
xo
Retrieved from https://www.google.com.ph/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&ved=0CC4QFjAB&url=https%3A%2F%2Fmrmcfarlane.wikispaces.com%2Ffile%2Fview%2FCircle.ppt&ei=a_dKUqXLPMiWiAeEt4HIBQ&usg=AFQjCNGbDDZoa7q3ckmyiIcYxpiS9l_U7A&bvm=bv.53371865,d.aGc September 27, 2013
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