Length of arc = (θ/360) x 2πr
Problem 1 :
A circle has an arc whose measure is 18° and whose length is 88π . Find
i) Radius ii) area of sector
Solution :
Arc measure = 18°
Length of arc = 88π
(θ/360) x 2πr = 88π
(18/360) x 2πr = 88π
r = 88/10
r = 8.8
Area of sector = (18/360) x π(8.8)^{2}
= 12.15
Problem 2 :
A circle has a circumference whose length is 25π . Find the area of sector whose central angle is 90°
Solution :
Arc measure = 90°
Length of arc = 25π
(θ/360) x 2πr = 25π
(90/360) x 2πr = 25π
r = 50
Area of sector = (90/360) x π(50)^{2}
= 625π
Problem 3 :
Find the measure of the central angle of an arc if its length is 14π and the radius is 18. Find the area of sector.
Solution :
radius = 18
Length of arc = 14π
(θ/360) x 2πr = 14π
(θ/360) x 2π x 18 = 14π
θ = 140
Area of sector = (θ/360) x πr^{2}
= (140/360) x π(18)^{2}
= 395.64
Find the area of sector RST in ⊙ S using the given information. Leave your answer in terms of π.
Problem 4 :
r = 3 in, mRT = 30
Solution:
Formula for area of a sector is given by
Substitute m∠RT = 30 and r = 3
Problem 5 :
r = 8 mm, mRT = 90
Solution:
Substitute m∠RT = 90 and r = 8
Problem 6 :
d = 10 ft, mTR = 180
Solution:
Formula for area of a sector is given by
Substitute m∠TR = 180 and d = 10
r = 10/2
r = 5
Problem 7 :
d = 13 m, mTR = 120
Solution:
Formula for area of a sector is given by
Substitute m∠TR = 120 and d = 13
r = 13/2
r = 6.5
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