If the radius of a circle is doubled, how is the length of the arc intercepted by a fixed central angle changed? Choose the correct answer below. A. The length remains the same. B. The length is doubled. C. The length is quadrupled.

Step 1 ：The problem is asking how the length of the arc intercepted by a fixed central angle changes if the radius of a circle is doubled.

Step 2 ：The length of an arc of a circle is given by the formula \(L = rθ\), where \(r\) is the radius of the circle and \(θ\) is the central angle in radians.

Step 3 ：If the radius is doubled, the length of the arc will also be doubled, assuming the central angle remains the same. This is because the length of the arc is directly proportional to the radius of the circle.

Step 4 ：Let's consider an example where the old radius is 1, the new radius is 2, and the angle is 1.

Step 5 ：Using the formula \(L = rθ\), the old arc length is \(1*1 = 1\) and the new arc length is \(2*1 = 2\).

Step 6 ：The ratio of the new arc length to the old arc length is \(2/1 = 2\). This means the arc length is doubled when the radius of the circle is doubled.

Step 7 ：\(\boxed{\text{Final Answer: B. The length is doubled.}}\)