A rectangular tank measures 2.4 m in length, 2 m in width, and 1.5 m in height. If the water level is currently at 0.45 m, how many litres of water are needed to fill the tank?

The volume of a rectangular tank is given by the formula $V = \text{length} \times \text{width} \times \text{height}$.

$$V_{total} = 2.4\, \text{m} \times 2\, \text{m} \times 1.5\, \text{m}$$ $$V_{total} = 7.2\, \text{m}^3$$

The water is up to a height of $0.45\, \text{m}$.

$$V_{current} = 2.4\, \text{m} \times 2\, \text{m} \times 0.45\, \text{m}$$ $$V_{current} = 2.16\, \text{m}^3$$

This is the difference between the total volume and the current volume.

$$V_{needed} = V_{total} - V_{current}$$ $$V_{needed} = 7.2\, \text{m}^3 - 2.16\, \text{m}^3$$ $$V_{needed} = 5.04\, \text{m}^3$$

Since $1\, \text{m}^3 = 1000\, \text{litres}$:

$$V_{needed\_litres} = 5.04\, \text{m}^3 \times 1000\, \frac{\text{litres}}{\text{m}^3}$$ $$V_{needed\_litres} = 5040\, \text{litres}$$

The amount of water needed to fill the tank is $\text{5040 litres}$.