1. **State the problem:** Lydia has a cuboid block with dimensions 35 cm by 40 cm by 25 cm. She melts it to make smaller cubes each with side length 4.5 cm. We need to find the maximum whole number of such cubes, $n$, that can be made. 2. **Formula and rules:** The volume of the cuboid is given by $$V_{cuboid} = l \times w \times h$$ where $l$, $w$, and $h$ are the length, width, and height. The volume of one small cube is $$V_{cube} = s^3$$ where $s$ is the side length of the cube. The maximum number of cubes is the integer part of the ratio of the cuboid volume to the cube volume: $$n = \left\lfloor \frac{V_{cuboid}}{V_{cube}} \right\rfloor$$ 3. **Calculate volumes:** $$V_{cuboid} = 35 \times 40 \times 25 = 35000 \text{ cm}^3$$ $$V_{cube} = 4.5^3 = 4.5 \times 4.5 \times 4.5 = 91.125 \text{ cm}^3$$ 4. **Calculate maximum number of cubes:** $$n = \left\lfloor \frac{35000}{91.125} \right\rfloor = \left\lfloor 384.07... \right\rfloor = 384$$ 5. **Answer:** The maximum whole number of small cubes that can be made is **384**.