A rectangular water reservoir contains 42000 litres of water . Find the depths of the water in the reservoir if its base measures 6 m by 3.5 m .

Answer

To find the depth of the water in the rectangular reservoir, we can follow these steps:

### Step-by-Step Solution:

1. **Convert Liters to Cubic Meters**:
We know that 1 cubic meter (m³) is equal to 1000 liters. Therefore, to convert 42000 liters to cubic meters:
\[ 42000 \text{ liters} = \frac{42000}{1000} \text{ m}^3 = 42 \text{ m}^3 \]

2. **Identify the Dimensions of the Base**:
The base of the reservoir measures 6 meters by 3.5 meters.

3. **Calculate the Area of the Base**:
The area (A) of the base can be calculated using the formula:
\[ A = \text{length} \times \text{width} = 6 \text{ m} \times 3.5 \text{ m} = 21 \text{ m}^2 \]

4. **Use the Volume Formula**:
The volume (V) of a rectangular prism (like our reservoir) is given by the formula:
\[ V = \text{Base Area} \times \text{Height} \]
Here, we can let the height (or depth) of the water be \( h \) meters. Therefore:
\[ V = 21 \text{ m}^2 \times h \text{ m} \]

5. **Set Up the Equation**:
According to the problem, the volume of water in the reservoir is 42 m³. Thus, we can set up the equation:
\[ 21h = 42 \]

6. **Solve for Depth (h)**:
To find \( h \), divide both sides of the equation by 21:
\[ h = \frac{42}{21} = 2 \text{ m} \]

### Final Answer:
The depth of the water in the reservoir is **2 meters**.

---