https://file.aiquickdraw.com/mathbot/file/17273252633435rs0bcoy.jpg

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!

A water basin in a rectangular solid shape had a base of 40 meters by 30 meters and a height of 50 meters. At the start of the month of no rain, the water basin was completely full. At the end of the month, the water level had dropped to a height of 38 meters. How many liters of water were used in the one-month period? Use 1 m^3 = 1,000 L.

Learn how to calculate the volume of water lost in a rectangular basin when the height drops from 50 meters to 38 meters. This problem involves calculating the volume of a prism, determining water loss, and converting cubic meters to liters. Suitable for students in Grades 8-10.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation