1. **State the problem:** Find the volume of a rectangular prism with dimensions 6 cm, 9 cm, and 4.5 cm. 2. **Formula:** The volume $V$ of a rectangular prism is given by the product of its length ($l$), width ($w$), and height ($h$): $$V = l \times w \times h$$ 3. **Plug in the values:** $$V = 6 \times 9 \times 4.5$$ 4. **Calculate step-by-step:** First multiply 6 and 9: $$6 \times 9 = 54$$ Then multiply the result by 4.5: $$54 \times 4.5$$ 5. **Simplify multiplication:** Express 4.5 as a fraction: $$4.5 = \frac{9}{2}$$ So, $$54 \times \frac{9}{2} = \frac{54 \times 9}{2} = \frac{486}{2}$$ 6. **Divide numerator and denominator by 2:** $$\frac{\cancel{486}^{243}}{\cancel{2}^1} = 243$$ 7. **Final answer:** The volume of the rectangular prism is $$\boxed{243 \text{ cubic centimeters}}$$