To find the radius of Circle O given that its circumference is 36π cm, we can use the formula for the circumference of a circle:
C = 2πr
In this formula, C represents the circumference and r is the radius of the circle. We can begin by substituting the known value of the circumference into the formula:
36π = 2πr
Next, we simplify this equation. We can divide both sides of the equation by π:
36 = 2r
Now, to solve for r, we divide both sides by 2:
r = 36 / 2
This leads us to:
r = 18
Therefore, the length of the radius r of Circle O is 18 cm.