1. **State the problem:** Find the volume of a rectangular prism with length $9$ cm, width $6$ cm, and height $4.5$ cm. 2. **Formula:** The volume $V$ of a rectangular prism is given by the formula: $$V = \text{length} \times \text{width} \times \text{height}$$ 3. **Plug in the values:** $$V = 9 \times 6 \times 4.5$$ 4. **Calculate step-by-step:** First multiply length and width: $$9 \times 6 = 54$$ Then multiply by height: $$54 \times 4.5 = 54 \times \frac{9}{2} = \cancel{54} \times \frac{9}{2} = 27 \times 9 = 243$$ 5. **Final answer:** The volume of the rectangular prism is **243 cubic centimeters**.