A circle with circumference 6 has an arc with a 20º central angle.

What is the length of the arc?

length of an arc = 1 / 3 unit or 0.3unit

Step-by-step explanation:

to calculate the length of an arc, having it in mind that the arc is a portion of the circumference of a circle.

circumference of a circle = 6unit

Ф = 20°

recall,

the formulae for finding the length of an arc

= 2πr (Ф/360)

assuming that r is the radius of the circle

so, the circumference of a circle is given to be = 2πr

6 = 2πr

r = (6/2π)

length of an arc = 2πr (Ф/360)

remember that r = (6/2π)

length of an arc = 2π (6/2π) [20°/360°]

length of an arc = 6 * 20°/360°

length of an arc = 120°/360°

length of an arc = 1/3unit