To find the length of minor arc SV in circle T with radius 24 inches and a central angle [tex]\(\theta = \frac{5\pi}{6}\)[/tex] radians, we use the formula for the arc length of a circle segment. The formula for the arc length [tex]\(L\)[/tex] is given by:
[tex]\[ L = r \cdot \theta \][/tex]
where:
- [tex]\( r \)[/tex] is the radius of the circle
- [tex]\(\theta \)[/tex] is the central angle in radians.
Given:
[tex]\[ r = 24 \, \text{inches} \][/tex]
[tex]\[ \theta = \frac{5\pi}{6} \, \text{radians} \][/tex]
Now, we substitute the given values into the arc length formula:
[tex]\[ L = 24 \cdot \frac{5\pi}{6} \][/tex]
To simplify this expression:
1. Multiply the constants:
[tex]\[ 24 \cdot \frac{5\pi}{6} = 24 \cdot \frac{5}{6} \cdot \pi \][/tex]
2. Simplify the fraction [tex]\(\frac{24 \cdot 5}{6}\)[/tex]:
[tex]\[ \frac{24 \cdot 5}{6} = 4 \cdot 5 = 20 \][/tex]
Thus:
[tex]\[ L = 20 \pi \][/tex]
So, the length of minor arc SV is:
[tex]\[ 20\pi \, \text{inches} \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{20 \pi \, \text{inches}} \][/tex]
