## Length of Arc

In this page length of arc we are going to see formula, example problems to understand this topic.

Length of arc = (θ/360) x 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

Length of-arc = (θ/360) x 2Πr

=  (90/360) x 2 x (22/7) x 7

=  (1/4) x 2 x 22

=   (1/2) x 22

=   11 cm

Example 2:

Find the length of-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) x l x r = 63

here r = 14 cm

(1/2) x l x 14 = 63

l x 7 = 63

l = 63/7

L = 9 cm

Therefore length of-arc 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

Length of-arc = (θ/360) x 2 Π r

L = (180/360) x 64

L = (1/2) x 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) x 20 x 7

=  10 x 7

= 70 square units.