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 

       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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Length of Arc to Formulas for Shapes