Answer :
To find the length of the minor arc [tex]\(SV\)[/tex] in the circle [tex]\(T\)[/tex] with a given radius and central angle, we will use the arc length formula for a circle. The formula is [tex]\( S = r \theta \)[/tex], where [tex]\( S \)[/tex] is the arc length, [tex]\( r \)[/tex] is the radius, and [tex]\( \theta \)[/tex] is the central angle in radians.
Let's break down the solution step by step:
1. Identify the radius:
The radius of circle [tex]\( T \)[/tex] is given as [tex]\( 24 \)[/tex] inches.
2. Identify the central angle:
The central angle [tex]\( \theta \)[/tex] is given in radians as:
[tex]\[ \theta = \frac{5 \pi}{6} \][/tex]
3. Apply the arc length formula:
We substitute the given values into the formula [tex]\( S = r \theta \)[/tex]:
[tex]\[ S = 24 \times \frac{5 \pi}{6} \][/tex]
4. Simplify the expression:
Simplify the multiplication:
[tex]\[ S = 24 \times \frac{5 \pi}{6} = 4 \times 5 \pi = 20 \pi \, \text{inches} \][/tex]
So, the length of the minor arc [tex]\( SV \)[/tex] is:
[tex]\[ 20 \pi \, \text{inches} \][/tex]
Therefore, the correct answer is:
[tex]\[ 20 \pi \, \text{inches} \][/tex]
Let's break down the solution step by step:
1. Identify the radius:
The radius of circle [tex]\( T \)[/tex] is given as [tex]\( 24 \)[/tex] inches.
2. Identify the central angle:
The central angle [tex]\( \theta \)[/tex] is given in radians as:
[tex]\[ \theta = \frac{5 \pi}{6} \][/tex]
3. Apply the arc length formula:
We substitute the given values into the formula [tex]\( S = r \theta \)[/tex]:
[tex]\[ S = 24 \times \frac{5 \pi}{6} \][/tex]
4. Simplify the expression:
Simplify the multiplication:
[tex]\[ S = 24 \times \frac{5 \pi}{6} = 4 \times 5 \pi = 20 \pi \, \text{inches} \][/tex]
So, the length of the minor arc [tex]\( SV \)[/tex] is:
[tex]\[ 20 \pi \, \text{inches} \][/tex]
Therefore, the correct answer is:
[tex]\[ 20 \pi \, \text{inches} \][/tex]
