1. **State the problem:** We are given a sector of a circle with an arc length $s = 4.5$ cm and radius $r = 3$ cm. We need to find the angle $\theta$ (in radians) subtended by the arc at the center of the circle. 2. **Formula used:** The arc length $s$ of a sector is related to the radius $r$ and the central angle $\theta$ by the formula: $$ s = r \theta $$ where $\theta$ is in radians. 3. **Rearrange the formula to find $\theta$:** $$ \theta = \frac{s}{r} $$ 4. **Substitute the given values:** $$ \theta = \frac{4.5}{3} = 1.5 \text{ radians} $$ 5. **Interpretation:** The angle subtended by the arc at the center of the circle is $1.5$ radians. 6. **Optional conversion to degrees:** Since $1$ radian $= \frac{180}{\pi}$ degrees, $$ \theta = 1.5 \times \frac{180}{\pi} \approx 85.94^\circ $$ **Final answer:** The angle subtended by the arc is $1.5$ radians (approximately $85.94^\circ$).