how to solve this?

Question

find the lenght of an arc with angle 120 degress in a circle with radius 3 meters. Round answer to 2 decimal places. If you need something related to pi, use pi=3.14159 or its exact  value.

Answer 1

L=length of arc

L=(120)/(180)*pi*3

L=(2/3)*pi*3

L=2 pi meters, or

L=2*3.14159

L=6.28318 meters

Answer 2

The arc length will be a fraction of the circumference, C = 2 pi r.

 

The fraction is 120°/360°, the portion of the circle that contains the arc.

 

The radius is 3 meters, so the arc length = 2 pi (3 meters)(120°/360°)

 

= 2 pi (3 meters)(1/3) = 2 pi meters exactly.

 

≈ 2*3.14159 ≈ 6.28 meters.

Answer 3

Hi Mark,

 

Length of an arc/circumference of the circle=n/360

 

Length of an arc/2πr=n/360

 

Length of an arc=(2πr×n)/360

 

                      =(2×3.14159×3×120)/360

 

                      =2×3.14159=6.28318 meters