To find the length of the minor arc SV in circle T with a given radius and central angle, we will use the arc length formula:
[tex]\[ \text{Arc Length} = \theta \times r \][/tex]
where [tex]\(\theta\)[/tex] is the central angle in radians, and [tex]\(r\)[/tex] is the radius of the circle.
Given:
- Radius, [tex]\(r = 24\)[/tex] inches
- Central angle, [tex]\(\theta = \frac{5\pi}{6}\)[/tex] radians
First, we substitute the given values into the arc length formula:
[tex]\[ \text{Arc Length} = \left( \frac{5\pi}{6} \right) \times 24 \][/tex]
To simplify:
[tex]\[ \text{Arc Length} = \frac{5\pi}{6} \times 24 = 5\pi \times 4 = 20\pi \][/tex]
Hence, the length of the minor arc SV is [tex]\(20\pi\)[/tex] inches.
Among the given options:
- [tex]\(20\pi\)[/tex] inches
- [tex]\(28\pi\)[/tex] inches
- [tex]\(40\pi\)[/tex] inches
- [tex]\(63\pi\)[/tex] inches
The correct answer is [tex]\(20\pi\)[/tex] inches.
