Angle Measure Worksheet With Answers - Section 6.1 Page 7
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10Area of a Circular Sector
2
The area of a circle of radius r is A = πr
. A sector of this circle with central
angle θ has an area that is the fraction θ/(2π) of the area of the entire circle
(see the Figure on the right). So the area of this sector is
θ
θ
1
× area of circle =
2
2
A =
(πr
) =
r
θ
2π
2π
2
◦
EXAMPLE: Find the area of a sector of a circle with central angle 60
if the radius of the circle
is 3 m.
Solution: To use the formula for the area of a circular sector, we must find the central angle of
( π
)
the sector in radians:
π
◦
60
= 60
rad =
rad
180
3
Thus, the area of the sector is
( π
)
1
1
3π
2
2
2
A =
r
θ =
(3)
=
m
2
2
3
2
◦
EXAMPLE: Find the area of a sector of a circle with central angle 4
if the radius of the circle
is 45 m.
Solution: To use the formula for the area of a circular sector, we must find the central angle of
( π
)
the sector in radians:
π
◦
4
= 4
rad =
rad
180
45
Thus, the area of the sector is
( π
)
1
1
45π
2
2
2
A =
r
θ =
(45)
=
m
2
2
45
2
EXAMPLE: A sprinkler on a golf course fairway is set to spray water over
◦
a distance of 70 feet and rotates through an angle of 120
(see the Figure
on the right). Find the area of the fairway watered by the sprinkler.
◦
Solution: First convert 120
to radian measure as follows.
( π
)
2π
◦
θ = 120
= 120
rad =
rad
180
3
(
)
Therefore
1
1
2π
4900π
≈ 5131 ft
2
2
2
A =
r
θ =
(70)
=
2
2
3
3
7
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