A circle has a radius of $10$ inches and a central angle of $3\mathrm{rad}$. What is the approximate length of the arc $s$ subtended by this angle? Choose the closest value.

• A. $5.23$ in.
• B. $52.36$ in.
• C. $104.67$ in.
• D. $41.87$ in.

Answer: (B)

Verified step by step guidance

1. Recall the formula for the length of an arc \(s\) in a circle, which is given by \(s = r \times \theta\), where \(r\) is the radius and \(\theta\) is the central angle in radians.
2. Identify the given values: the radius \(r = 10\) inches and the central angle \(\theta = 3\) radians.
3. Substitute the given values into the arc length formula: \(s = 10 \times 3\).
4. Multiply the radius by the angle to find the arc length: \(s = 30\) inches (this is the exact value before approximation).
5. Compare the calculated arc length with the provided options to choose the closest value.