LENGTH OF ARC
Length of arc :
Here we are going to see some example problems based on finding the length of arc.
(θ/360) ⋅ 2Πr
here θ - central angle
r - radius
Now we are going to see example problems based on this formula.
Example 1 :
Find the length of arc whose radius is 7 cm and central angle 90 degree
Solution :
Here θ = 90 degree
r = 7 cm
Arc length = (θ/360) ⋅ 2Πr
= (90/360) ⋅ 2 ⋅ (22/7) ⋅ 7
= (1/4) ⋅ 2 ⋅ 22
= (1/2) ⋅ 22
= 11 cm
Example 2:
Find the length of an arc if the radius of circle is 14 cm and area of circle is 63 square cm.
Solution :
Area of the circle = 63 square cm
Area of circle = (1/2) l r
(1/2) ⋅ l ⋅ r = 63
here r = 14 cm
(1/2) ⋅ l ⋅ 14 = 63
l ⋅ 7 = 63
L = 9 cm
Hence the required arc length is 9 cm.
Example 3 :
Find the length of arc if the perimeter of a sector is 45 cm and radius is 10 cm.
Solution :
Perimeter of sector = 45 cm
L + 2r = 45
here r = 10 cm
L + 2 (10) = 45
L + 20 = 45
L = 45 - 20
L = 25 cm
Example 4 :
Find the arc length whose central angle is 180 degree and perimeter of circle is 64 cm
Solution :
Perimeter of circle = 64 cm
2 Π r = 64
Arc length = (θ/360) ⋅ 2 Π r
l = (180/360) ⋅ 64
l = (1/2) ⋅ 64
l = 32 cm
Example 5 :
Find the area of the sector whose arc length is 20 cm and radius is 7 cm.
Solution :
Arc length (L) = 20 cm
r = 7 cm
Area of sector = (1/2) lr
= (1/2) ⋅ 20 ⋅ 7
= 10 x 7
= 70 square units.
After having gone through the problems explained above, we hope that the students would have understood the stuff given on length of arc.
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