To find the length of the arc created by a central angle in radians, you can use the formula:
\[ \text{Arc Length} = r \cdot \theta \]
where \( r \) is the radius and \( \theta \) is the central angle in radians.
In this case, the radius \( r \) is 30 inches, and the central angle \( \theta \) is \( \frac{5\pi}{3} \) radians.
Now, substitute the values into the formula:
\[ \text{Arc Length} = 30 \cdot \frac{5\pi}{3} \]
Calculating this:
\[ \text{Arc Length} = 30 \times \frac{5\pi}{3} = 10 \times 5\pi = 50\pi \text{ inches} \]
So, the length of the arc is \( 50\pi \) inches.
The correct response is:
50π