Final answer:
The arc length in a circle is directly proportional to the radius, and it increases with the radius, which means that at a constant angle, a larger radius will result in a longer arc length.
Step-by-step explanation:
The relationship between the arc length and the radius of a circle is an important concept in mathematics. When the radius of a circle is rotated through a specific angle (denoted A0 in Figure 6.3), the arc length As is the length of the path along the circumference that corresponds to this angle. This arc length is directly proportional to the radius of the circle. In other words, as the radius increases, the arc length also increases, providing the angle through which the radius rotates remains constant.
So, the correct explanation for how the arc length compares to the circle's radius is: The arc length is directly proportional to the radius of the circular path, and it increases with the radius. This means that if you imagine two points on a CD (representing a circle), both rotating through the same angle, the one near the outer edge would trace a greater arc length compared to the one near the center, due to having a larger radius of curvature.