1. **State the problem:** Find the radius of a circle given its circumference is 106.81 cm. 2. **Formula used:** The circumference $C$ of a circle is given by the formula $$C = 2\pi r$$ where $r$ is the radius. 3. **Rearrange the formula to solve for $r$:** $$r = \frac{C}{2\pi}$$ 4. **Substitute the given circumference:** $$r = \frac{106.81}{2\pi}$$ 5. **Calculate the denominator:** $$2\pi \approx 6.2832$$ 6. **Divide to find $r$:** $$r = \frac{106.81}{6.2832}$$ 7. **Show cancellation step:** $$r = \frac{\cancel{106.81}}{\cancel{6.2832}}$$ (just indicating division) 8. **Final calculation:** $$r \approx 17.0$$ centimeters. **Answer:** The radius of the circle is approximately 17.0 cm.