Find the arc length and the area of a sector of a circle of

Find the arc length and the area of a sector of a circle of radius 50 corresponding to

a) A full revolution

b) A central angle of 25 degrees 20\'

Solution

Formula for finding arc length is = r (in radians)

Where is angle of revolution and r s radius as shown in diagram below.

                                                                                                                                                                                                                                                                                       Case a: When full revolution.

That means arc makes complete revolutuion. Means the angle = 2 radians     

Given radius, r= 50

The arc length is = r = 2 X 50 = 100 radians                                                

Case b: When central angle of 25 degrees 20\'

That is = 25 degrees 20 radians

We will convert all degrees into radians.

We know that 1 radian = 180º/

       Or 1º = / 180 radians                                                                                       

Accordingly 25 º = 25 X ( / 180) radians

                             = (0.138) X                (as 25 / 180 = 0.138)

                               = 0.436 radians     (as =3.14)

As = 25 degrees 20 radians

        = 0.436 + 20 radians

         = 20.436

The arc length is = r = 20.436 X 50 = 1021.8 radians