A circle has a central angle measuring \( \frac{7 \pi}{6} \) radians that intersects an arc of length 18 cm . What is the length of the radiu of the circle? Round your answer to the nearest tenth. Use 3.14 for \( \pi \). 3.7 cm 4.9 cm 14.3 cm 15.4 cm

To find the radius of the circle, we can use the formula that relates the arc length \( s \), the radius \( r \), and the central angle \( \theta \) in radians: \[ s = r\theta \] Rearranging this formula gives us \( r = \frac{s}{\theta} \). We know the arc length \( s \) is 18 cm and the central angle \( \theta \) is \( \frac{7\pi}{6} \) radians. Plugging in the numbers: \[ r = \frac{18}{\frac{7\pi}{6}} = \frac{18 \times 6}{7\pi} = \frac{108}{7\pi} \] Now substituting \( \pi \) with 3.14: \[ r \approx \frac{108}{7 \times 3.14} = \frac{108}{21.98} \approx 4.9 \text{ cm} \] So, rounding to the nearest tenth, the radius of the circle is approximately 4.9 cm. To double-check our calculations, we re-evaluate step by step. Confirm that multiplying 7 and 3.14 indeed gives 21.98, and dividing 108 by this value does yield about 4.9. In practical applications, it's always a good move to verify your work, especially on tests! Keep an eye out for rounding—using more decimal places can help accuracy.