To find the length of the minor arc [tex]\( \overset{\frown}{SV} \)[/tex] in a circle, we can use the formula for the length of an arc, which is given by:
[tex]\[ \text{Length of arc} = r \theta \][/tex]
where [tex]\( r \)[/tex] is the radius of the circle and [tex]\( \theta \)[/tex] is the central angle in radians.
Given the details:
- The radius [tex]\( r \)[/tex] of the circle is [tex]\( 24 \)[/tex] inches.
- The central angle [tex]\( \theta \)[/tex] is [tex]\( \frac{5 \pi}{6} \)[/tex] radians.
Let's substitute these values into the formula:
[tex]\[ \text{Length of minor arc SV} = 24 \times \frac{5 \pi}{6} \][/tex]
We can simplify the computation inside the multiplication:
[tex]\[ \text{Length of minor arc SV} = 24 \times \frac{5 \pi}{6} \][/tex]
[tex]\[ = 24 \times \frac{5 \pi}{6} \][/tex]
[tex]\[ = 24 \times \frac{5 \pi}{6} \][/tex]
[tex]\[ = 4 \times 5 \pi \][/tex]
[tex]\[ = 20 \pi \][/tex]
So, the length of the minor arc [tex]\( \overset{\frown}{SV} \)[/tex] is [tex]\( 20 \pi \)[/tex] inches.
Therefore, the correct answer is:
[tex]\[ 20 \pi \text{ inches} \][/tex]
