If a circle has a radius of $r$ inches and a central angle of $\theta$ radians, what is the length of arc $\mathrm{zv}$ in inches?

• A. $\frac{2\pi r}{\theta }$
• B. $\frac{\theta }{2r}$
• C. $r\cdot \theta$
• D. $r+\theta$

Answer: (C)

Verified step by step guidance

1. Recall the formula for the length of an arc (s) of a circle, which is given by the product of the radius (r) and the central angle (θ) in radians: \(s = r \cdot \theta\).
2. Understand that the central angle θ must be in radians for this formula to apply directly; if given in degrees, convert it to radians first.
3. Identify the given values: radius \(r\) inches and central angle \(\theta\) radians.
4. Substitute the given values into the formula: \(s = r \cdot \theta\).
5. Express the arc length \(zv\) as \(zv = r \cdot \theta\), which gives the length of the arc in inches.