In a circle with center $O$ and radius $20$ inches, if the measure of angle $SOV$ is $72°$, what is the length of minor arc $SV$?

• A. $40\pi$ in.
• B. $63$ in.
• C. $20\pi$ in.
• D. $28\pi$ in.

Answer: (A)

Verified step by step guidance

1. Identify the given information: the radius of the circle \(r = 20\) inches and the central angle \(\angle SOV = 72^\circ\).
2. Recall the formula for the length of an arc \(L\) in a circle: \(L = r \times \theta\), where \(\theta\) is the central angle in radians.
3. Convert the central angle from degrees to radians using the conversion factor \(\pi\) radians = \$180^\circ\(: \)\theta = 72^\circ \times \frac{\pi}{180^\circ}$.
4. Substitute the radius and the radian measure of the angle into the arc length formula: \(L = 20 \times \left(72 \times \frac{\pi}{180}\right)\).
5. Simplify the expression to find the length of the minor arc \(SV\).