Final answer:
The length of the radius of the circle is 4 units, found by using the circumference formula C = 2πr and the given length of the semi-circular arc ADB, which is 8π.
Step-by-step explanation:
If in a circle segment AB is a diameter and the length of arc ADB is 8 pi, to find the length of the radius of the circle, we can use the circumference formula.
The circumference of a circle is calculated by C = 2πr, where C is the circumference and r is the radius. Since AB is the diameter, and arc ADB represents half of the circle's circumference, we have:
Arc ADB = πd
Since d = 2r, then Arc ADB = 2πr
Given that Arc ADB = 8π, we can set 2πr equal to 8π
By dividing both sides by 2π, we find r = 4
Therefore, the radius r of the circle is 4 units.