A circle has a central angle of \( \frac{5 \pi}{2} \) radians that intercepts an arc with a length of 46 inches. Based on this information, what is the measure of the radius of the circle? Round to the nearest hundredth (two decimal places).

Step 1 ：1. \( \frac{5 \pi}{2} \) radians represents a central angle of the circle, with an intercepted arc of 46 inches in length. We need to find the radius of the circle.

Step 2 ：2. Use the arc length formula: \( L = r \theta \), where \(L\) is the arc length, \(r\) is the radius, and \(\theta\) is the central angle in radians.

Step 3 ：3. Substitute the given values: \( 46 = r \left( \frac{5 \pi}{2} \right) \).

Step 4 ：4. Solve for \(r\): \( r = \frac{46}{\frac{5 \pi}{2}} \).

Step 5 ：5. Multiply both sides by \( \frac{2}{5 \pi} \) to get \( r \approx 5.85 \) inches.