Consider circle T with a radius of 24 inches and [tex]$\theta=\frac{5 \pi}{6}$[/tex] radians.

What is the length of the minor arc SV?

A. [tex]$20 \pi$[/tex] in.
B. [tex]$28 \pi$[/tex] in.
C. [tex]$40 \pi$[/tex] in.
D. [tex]$63 \pi$[/tex] in.



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].