PERIMETER OF SECTOR WORKSHEET
Problem 1 :
Find the perimeter of the sector PQR shown below.
Problem 2 :
Find the perimeter of the sector AOB shown below.
Problem 3 :
Find the perimeter of the sector BAP shown below.
Problem 4 :
Find the perimeter of the sector PQR shown below.
Problem 5 :
Find the perimeter of sector whose area is 324 square cm and the radius is 27 cm.
Problem 6 :
Find the length of arc, if the perimeter of sector is 45 cm and radius is 10 cm.
Problem 7 :
Find the radius of sector whose perimeter of the sector is 30 and length of the arc is 16 cm.
Problem 8 :
Find the diameter of the circle which has a sector whose perimeter is 84 cm and length of arc of the sector is 56 cm.
Solutions
Problem 1 :
Find the perimeter of the sector PQR shown below.
Solution :
Length of the arc is
l = θ/360° ⋅ 2∏r
Substitute θ = 60°, r = 42 and ∏ = 22/7.
l = 60°/360° ⋅ 2 ⋅ 22/7 ⋅ 42
l = 1/6 ⋅ 2 ⋅ 22 ⋅ 6
l = 1 ⋅ 2 ⋅ 22
l = 44 cm
Perimeter of sector is
= l + 2r
Substitute l = 44 and r = 42.
= 44 + 2(42)
= 44 + 84
= 128 cm
So, length of the arc is 128 cm.
Problem 2 :
Find the perimeter of the sector AOB shown below.
Solution :
Length of the arc is
l = θ/360° ⋅ 2∏r
Substitute θ = 120°, r = 21 and ∏ = 22/7.
l = 120°/360° ⋅ 2 ⋅ 22/7 ⋅ 21
l = 1/3 ⋅ 2 ⋅ 22 ⋅ 3
l = 1 ⋅ 2 ⋅ 22
l = 44 cm
Perimeter of sector is
= l + 2r
Substitute l = 44 and r = 21.
= 44 + 2(21)
= 44 + 42
= 86 cm
So, length of the arc is 86 cm.
Problem 3 :
Find the perimeter of the sector BAP shown below.
Solution :
Length of the arc is
l = θ/360° ⋅ 2∏r
Substitute θ = 72°, r = 35 and ∏ = 22/7.
l = 72°/360° ⋅ 2 ⋅ 22/7 ⋅ 35
l = 1/5 ⋅ 2 ⋅ 22 ⋅ 5
l = 1 ⋅ 2 ⋅ 22
l = 44 cm
Perimeter of sector is
= l + 2r
Substitute l = 44 and r = 35.
= 44 + 2(35)
= 44 + 70
= 114 cm
So, length of the arc is 114 cm.
Problem 4 :
Find the perimeter of the sector PQR shown below.
Solution :
Length of the arc is
l = θ/360° ⋅ 2∏r
Substitute θ = 36°, r = 10.5 and ∏ = 22/7.
l = 36°/360° ⋅ 2 ⋅ 22/7 ⋅ 10.5
l = 1/10 ⋅ 2 ⋅ 22 ⋅ 1.5
l = 66/10
l = 6.6 cm
Perimeter of sector is
= l + 2r
Substitute l = 6.6 and r = 10.5.
= 6.6 + 2(10.5)
= 6.6 + 21
= 27.6 cm
So, length of the arc is 27.6 cm.
Problem 5 :
Find the perimeter of sector whose area is 324 square cm and the radius is 27 cm.
Solution :
Area of sector = 324 cm2
rl / 2 = 324
Multiply each side by 2.
rl = 648
Substitute 27 for r.
27l = 648
Divide each side by 27.
l = 24 cm
Perimeter of sector is
= l + 2r
= 24 + 2(27)
= 24 + 54
= 78 cm
Problem 6 :
Find the length of arc, if the perimeter of sector is 45 cm and radius is 10 cm.
Solution :
Perimeter of sector = 45 cm
l + 2r = 45
Substitute 10 for r.
l + 2 (10) = 45
l + 20 = 45
l = 45 - 10
l = 35 cm
Problem 7 :
Find the radius of sector whose perimeter of the sector is 30 cm and length of the arc is 16 cm.
Solution :
Perimeter of sector = 30 cm
l + 2r = 30
Substitute 16 for l.
16 + 2r = 30
Subtract 16 from each side.
2r = 14
Divide each side by 2.
r = 7 cm
Problem 8 :
Find the diameter of the circle which has a sector whose perimeter is 84 cm and length of arc of the sector is 56 cm.
Solution :
Perimeter of sector = 84 cm
l + 2r = 84
Substitute 56 for l.
56 + 2r = 84
Subtract 56 from each side.
2r = 28
Diameter = 2 x Radius
Diameter = 2r
Diameter = 28 cm.
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