Let's break down the problem step-by-step to determine how many liters of water were used in the one-month period:

1. Initial Volume of the Water Basin (at full capacity):

The basin has a base of $40 \, \text{m} \times 30 \, \text{m}$ and an initial height of 50 meters.

• Base Area = $40 \times 30 = 1,200 \, \text{m}^2$
• Initial Volume (when full) = Base Area $\times$ Height $\text{Initial Volume} = 1,200 \, \text{m}^2 \times 50 \, \text{m} = 60,000 \, \text{m}^3$

2. Final Volume of the Water Basin (after one month):

After a month, the water height dropped to 38 meters.

• Final Volume = Base Area $\times$ New Height $\text{Final Volume} = 1,200 \, \text{m}^2 \times 38 \, \text{m} = 45,600 \, \text{m}^3$

3. Amount of Water Lost:

The amount of water lost is the difference between the initial and final volumes. $\text{Water Lost} = 60,000 \, \text{m}^3 - 45,600 \, \text{m}^3 = 14,400 \, \text{m}^3$

4. Convert to Liters:

Since $1 \, \text{m}^3 = 1,000 \, \text{L}$, $14,400 \, \text{m}^3 = 14,400,000 \, \text{L}$

Thus, the amount of water used during the one-month period is 14,400,000 liters.

Answer:

The correct option is 14,400,000 liters.

Would you like any more details or further explanation? Here are some related questions:

1. How do you calculate the volume of a rectangular prism?
2. How would the volume change if the base dimensions were different?
3. What would happen if the height dropped by more than 12 meters?
4. How does the conversion from cubic meters to liters work?
5. How much water would be used if the final height was 40 meters?

Tip: Always ensure that units are consistent when working with volume and capacity calculations!