1. **State the problem:** We have a circle with radius $5$ cm. We want to find the length of arcs corresponding to angles of $1$ radian and $2.2$ radians. 2. **Formula used:** The length $s$ of an arc in a circle is given by the formula: $$s = r \times \theta$$ where $r$ is the radius and $\theta$ is the angle in radians. 3. **Calculate the arc length for $1$ radian:** $$s = 5 \times 1 = 5 \text{ cm}$$ 4. **Calculate the arc length for $2.2$ radians:** $$s = 5 \times 2.2 = 11 \text{ cm}$$ 5. **Explanation:** The radian measure directly relates the angle to the arc length by multiplying the radius by the angle in radians. **Final answers:** - Arc length for $1$ radian is $5$ cm. - Arc length for $2.2$ radians is $11$ cm.