To find the length of the minor arc [tex]\( SV \)[/tex] in a circle [tex]\( T \)[/tex] with radius 24 inches and a central angle [tex]\( \theta = \frac{5\pi}{6} \)[/tex] radians, we use the formula for the arc length [tex]\( L \)[/tex]:
[tex]\[ L = r \times \theta \][/tex]
where [tex]\( r \)[/tex] is the radius of the circle and [tex]\( \theta \)[/tex] is the measure of the central angle in radians.
Given:
- [tex]\( r = 24 \)[/tex] inches
- [tex]\( \theta = \frac{5\pi}{6} \)[/tex] radians
By substituting the given values into the formula, we get:
[tex]\[ L = 24 \times \frac{5\pi}{6} \][/tex]
To simplify the multiplication:
[tex]\[ L = 24 \times \frac{5\pi}{6} = 24 \times \frac{5}{6} \times \pi = 4 \times 5 \times \pi = 20\pi \][/tex]
So, the length of the minor arc [tex]\( SV \)[/tex] is:
[tex]\[ 20\pi \ \text{inches} \][/tex]
Therefore, the correct answer is [tex]\( 20\pi \)[/tex] inches.
