1. **Problem Statement:** (a) Find the height of a cuboid suitcase with length 40 cm, width 24 cm, and maximum volume 52800 cm³. 2. **Formula:** Volume of cuboid = length × width × height 3. **Calculation:** Given volume $V = 52800$ cm³, length $l = 40$ cm, width $w = 24$ cm. Use formula: $$V = l \times w \times h$$ $$52800 = 40 \times 24 \times h$$ 4. **Simplify:** $$52800 = 960 \times h$$ Divide both sides by 960: $$\cancel{960} \times h = \frac{52800}{\cancel{960}}$$ $$h = 55$$ 5. **Answer:** The height of the suitcase is **55 cm**.