Answer :
To determine the length of the minor arc SV in circle \( T \) with a given radius of 24 inches and angle \(\theta = \frac{5 \pi}{6}\) radians, we follow these steps:
1. Understand the formula for the length of an arc: The formula to calculate an arc length \( L \) of a circle is given by:
[tex]\[ L = r \theta \][/tex]
where \( r \) is the radius of the circle and \( \theta \) is the central angle in radians.
2. Substitute the given values: In this problem, the radius \( r \) is 24 inches and the angle \( \theta \) is \(\frac{5 \pi}{6}\) radians.
3. Calculate the arc length:
[tex]\[ L = 24 \times \frac{5 \pi}{6} \][/tex]
4. Simplify the expression:
[tex]\[ L = 24 \times \frac{5}{6} \pi = 4 \times 5 \pi = 20 \pi \text{ inches} \][/tex]
Therefore, the length of the minor arc [tex]\( SV \)[/tex] is [tex]\( \boxed{20 \pi \text{ inches}} \)[/tex].
1. Understand the formula for the length of an arc: The formula to calculate an arc length \( L \) of a circle is given by:
[tex]\[ L = r \theta \][/tex]
where \( r \) is the radius of the circle and \( \theta \) is the central angle in radians.
2. Substitute the given values: In this problem, the radius \( r \) is 24 inches and the angle \( \theta \) is \(\frac{5 \pi}{6}\) radians.
3. Calculate the arc length:
[tex]\[ L = 24 \times \frac{5 \pi}{6} \][/tex]
4. Simplify the expression:
[tex]\[ L = 24 \times \frac{5}{6} \pi = 4 \times 5 \pi = 20 \pi \text{ inches} \][/tex]
Therefore, the length of the minor arc [tex]\( SV \)[/tex] is [tex]\( \boxed{20 \pi \text{ inches}} \)[/tex].
