To find length of arc of a sector, we will use the formula
s = rθ
Length of arc is part of the circumference of the circle, the picture clearly shows.
s = (θ/360) ∙ 2πr
Problem 1:
Find the length of arc AB.
Solution:
The formula to find the arc length is
= (Arc Measure / 360˚) ∙ 2πr
Substitute r = 6 cm, arc measure = 120˚ and π = 3.14
= (120˚/360˚) × 2 × 3.14 × 6
= 1/3 × 37.68
= 12.56 cm
So, the length of the arc is about 12.56 cm.
Problem 2:
The diameter is 24 cm. Find the length of arc CD.
Solution :
The formula to find the arc length is
= (Arc Measure / 360˚) ∙ 2πr
Diameter = 24 cm
Substitute r = 12 cm, arc measure = 60˚ and π = 3.14
= (60˚/360˚) × 2 × 3.14 × 12
= 1/6 × 75.36
= 12.56 cm
So, the length of the arc is about 12.56 cm.
Problem 3:
The length of arc EF is 5π in. find the length of the radius.
Solution :
The formula to find the arc length is
= (Arc Measure / 360˚) ∙ 2πr
Substitute length of arc = 5π in, arc measure = 30˚ and π = 3.14
5π = (30˚/360˚) × 2 × π × r
5π = 1/6 × π × r
r = 30 in
So, the length of the radius is about 30 in.
Problem 4:
Find the length of arc XY.
Solution :
The formula to find the arc length is
= (Arc Measure / 360˚) ∙ 2πr
Substitute r = 10 cm, arc measure = 70˚ and π = 3.14
= (70˚/360˚) × 2 × 3.14 × 10
= 12.21 cm
So, the length of the arc is about 12.21 cm.
Problem 5 :
A circle has an arc whose measure is 80˚ and whose length is 88π. What is the diameter of the circle?
Solution :
The formula to find the arc length is
= (Arc Measure / 360˚) ∙ 2πr
Substitute length of arc = 88π, arc measure = 80˚ and π = 3.14
88π = (80˚/360˚) × 2 × π × r
88π = 4/9 × π × r
r = 198
Diameter = 2 × radius
Diameter = 2 × 198
Diameter = 396
So, diameter of the circle is 396.
Problem 6 :
A circle has a circumference whose length is 25π. Find the length of an arc whose central angle is 90˚.
Solution :
The formula to find the arc length is
= (Arc Measure / 360˚) ∙ 2πr
Substitute circumference = 25π, arc measure = 90˚
= (90˚/360˚) × 25π
= 1/4 × 25π
= 6.25π
So, length of an arc is 6.25π.
Problem 7 :
Find the measure of the central angle of an arc if its length is 14π and the radius is 18.
Solution :
Arc length = 14π and radius = 18
The formula to find the arc length is
14 π = (Arc Measure / 360˚) ∙ 2πr
14 π = (Arc Measure / 360˚) ∙ 2 × π × 18
Arc measure = (14π × 360)/2 × π × 18
= 140˚
So, measure of the central angle of an arc is 140˚.
May 21, 24 08:51 PM
May 21, 24 08:51 AM
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