Answer:
We can use the formula to find the length of a circular arc given the measure of the central angle and the radius:
Length of arc = (central angle measure / 360) x 2πr
where r is the radius of the circle.
Given that the central angle measure is 40° and the length of the arc is 6 cm, we can set up the equation:
6 = (40/360) x 2πr
Simplifying the fraction and solving for r, we get:
6 = (1/9) x 2πr
r = 9 x 6 / 2π
r = 27/π
So the radius of the circle is 8.59 cm (rounded to two decimal places).