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

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

** 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.

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