LENGTH OF ARC

Length of arc :

Here 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.

After having gone through the stuff given above, we hope that the students would have understood "Length of arc"

Apart from the stuff given above, if you want to know more about "Length of a arc", please click here.

Apart from the stuff given in this section, if you need any other stuff in math, please use our google custom search here. 

Widget is loading comments...