1. **State the problem:** We need to find the volume of a rectangular prism made up of unit cubes, where each cube has side length 1 cm. 2. **Given dimensions:** The prism is 3 cubes tall, 3 cubes wide, and 5 cubes long. 3. **Formula for volume of a rectangular prism:** $$\text{Volume} = \text{length} \times \text{width} \times \text{height}$$ 4. **Apply the formula:** $$\text{Volume} = 5 \times 3 \times 3$$ 5. **Calculate:** $$\text{Volume} = 45$$ 6. **Interpretation:** Since each cube is 1 cm³, the total volume is 45 cm³. **Final answer:** The volume of the rectangular prism is $45$ cubic centimeters.