1. **State the problem:** We are given a tank with dimensions length $L=50$ cm, width $W=110$ cm, and height $H=30$ cm. We need to calculate the volume of the tank and then find the height of water if there are 40 liters of water in the tank. 2. **Calculate the volume of the tank:** The volume $V$ of a rectangular cuboid is given by the formula: $$V = L \times W \times H$$ Substitute the values: $$V = 50 \times 110 \times 30$$ Calculate: $$V = 165000 \text{ cm}^3$$ 3. **Convert liters to cubic centimeters:** Since 1 liter = 1000 cm³, 40 liters = $$40 \times 1000 = 40000 \text{ cm}^3$$ 4. **Calculate the height of water in the tank:** Let the height of the water be $h$. The volume of water is: $$V_{water} = L \times W \times h$$ Rearranged to find $h$: $$h = \frac{V_{water}}{L \times W}$$ Substitute the known values: $$h = \frac{40000}{50 \times 110}$$ Simplify the denominator: $$h = \frac{40000}{5500}$$ Cancel common factors: $$h = \frac{\cancel{40000}}{\cancel{5500}} = \frac{40000 \div 500}{5500 \div 500} = \frac{80}{11}$$ Calculate the decimal value: $$h \approx 7.27 \text{ cm}$$ **Final answer:** The height of the water in the tank is approximately $7.27$ cm.