how to work this

Question

find the length of an arc with angle 120 degress in a circle with radius 12 meters. round answer to 2 decimal places.

Answer 1

We want 120/360 parts of the circumference of a circle with radius 12 meters.

 

arc length = (1/3)(2 pi)(12 m) = 8 pi ≈ 25.13274122871834 ≈ 25.13 m

Answer 2

The length of an arc is equal to the angle/360 X the circumference (2pi x r). 

 

L = 120/360 x 2pi x 12

L = 1/3 X 24pi 

L = 8 pi 

Answer 3

Length of an Arc (L) = n^° × 2πr

                                360^°

 

given

n° = 120

r = 12

π = 3.142

 

Solving

 

L =  120 × 2(3.142)(12)

       360

 

L = 1 × 2(37.704)

      3

 

L = 1 × 75.408

      3

 

L = 75.408

          3

 

L = 25.136

 

Rounding to 2 decimal places we'd have;

 

L = 25.14