Final answer:
To find the length of a 135 degrees arc, you need to calculate the circumference of the circle and use the formula for arc length. The length of the arc is 4 * pi / 3 kilometers.
Step-by-step explanation:
To find the length of a 135 degrees arc on a circle with a radius of 4 kilometers, we need to use the formula for arc length.
The formula is given by:
arc length = (angle/360) * circumference.
In this case, the angle is 135 degrees and the radius is 4 kilometers.
The circumference of a circle can be calculated using the formula: circumference = 2 * pi * radius. Plugging in the values, we can calculate the length of the arc as follows:
circumference = 2 * pi * 4 = 8 * pi kilometers
arc length = (135/360) * (8 * pi) = 3 * (8 * pi) / 6 = 4 * pi / 3 kilometers