Find the length of the arc, \( s \), on a circle of radius r intercepted by a central angle \( \theta \). Express the arc length in terms of \( \pi \). Then round your answer to two decimal places. Radius, \( r=20 \) inches; Central angle, \( \theta=10^{\circ} \) \( s=\square \) inches (Simplify your answer. Type an exact answer in terms of \( \pi \). Use integers or fractions for any numbers in the expression.) \( s=\square \) inches

To find the length of the arc \( s \) on a circle of radius \( r \) intercepted by a central angle \( \theta \), we can use the formula: \[ s = r \theta \] However, the angle \( \theta \) must be in radians. To convert degrees to radians, we use the conversion factor: \[ \text{radians} = \text{degrees} \times \frac{\pi}{180} \] Given that \( \theta = 10^\circ \), we can convert it to radians: \[ \theta = 10 \times \frac{\pi}{180} = \frac{10\pi}{180} = \frac{\pi}{18} \text{ radians} \] Now, substituting the values of \( r \) and \( \theta \) into the arc length formula: \[ s = r \theta = 20 \times \frac{\pi}{18} \] Simplifying this expression: \[ s = \frac{20\pi}{18} = \frac{10\pi}{9} \] Thus, the exact length of the arc in terms of \( \pi \) is: \[ s = \frac{10\pi}{9} \text{ inches} \] Now, to round this to two decimal places, we first calculate the numerical value: \[ s \approx \frac{10 \times 3.14159}{9} \approx \frac{31.4159}{9} \approx 3.49 \text{ inches} \] So, the final answers are: Exact answer: \[ s = \frac{10\pi}{9} \text{ inches} \] Rounded answer: \[ s \approx 3.49 \text{ inches} \]