## 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

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

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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