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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