To find the length of the arc, you can use the formula:
Arc Length = (Central Angle / 360 degrees) x (2Ï€ x Radius)
In this case, the central angle is given as 20 degrees, and the radius is given as 3.
Substituting these values into the formula:
Arc Length = (20 degrees / 360 degrees) x (2Ï€ x 3)
To simplify, convert the angle to radians by multiplying by π/180:
Arc Length = (20 degrees x π/180) x (2π x 3)
Arc Length = (20Ï€/180) x (2Ï€ x 3)
Now, simplify the equation:
Arc Length = (1/9)Ï€ x (6Ï€)
Arc Length = 6π² / 9
Finally, divide by 9 and multiply by π to get the length of the arc:
Arc Length ≈ (6π² / 9) ≈ 6.28319 units (rounded to five decimal places)
Therefore, the length of the arc is approximately 6.28319 units.