To find the length of the minor arc [tex]\( SV \)[/tex] in circle [tex]\( T \)[/tex], you need to use the formula for the arc length of a circle, which is given by:
[tex]\[ \text{Arc Length} = \theta \times r \][/tex]
where:
- [tex]\( \theta \)[/tex] is the central angle in radians
- [tex]\( r \)[/tex] is the radius of the circle
In this problem, the radius [tex]\( r \)[/tex] of the circle is given as [tex]\( 24 \)[/tex] inches, and the central angle [tex]\( \theta \)[/tex] is given as [tex]\( \frac{5 \pi}{6} \)[/tex] radians.
Substitute these values into the formula:
[tex]\[ \text{Arc Length} = \frac{5 \pi}{6} \times 24 \][/tex]
Now, multiply these numbers:
[tex]\[ \text{Arc Length} = \frac{5 \pi}{6} \times 24 = 20 \pi \][/tex]
To ascertain the right answer choice, compare [tex]\( 20 \pi \)[/tex] with the given options:
- [tex]\( 20 \pi \)[/tex] in.
- [tex]\( 28 \pi \)[/tex] in.
- [tex]\( 40 \pi \)[/tex] in.
- [tex]\( 63 \pi \)[/tex] in.
The correct answer is:
[tex]\[ 20 \pi \text{ in.} \][/tex]
Thus, the length of the minor arc [tex]\( SV \)[/tex] is [tex]\( 20 \pi \)[/tex] inches.
