A rectangular water reservoir contains 42,000 litres of water. Find the depth of water in the reservoir, if the base measures 6 by 3.5m.

Options

A. 1 m
B. 2.5 m
C. 3 m
D. 2 m

Answer

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

### Step 1: Understand the Volume of Water
The volume of water in the reservoir is given as 42,000 liters. We need to convert this volume into cubic meters, as the dimensions of the base are in meters.

**Conversion:**
1 cubic meter = 1,000 liters
So,
\[ 42,000 \text{ liters} = \frac{42,000}{1,000} = 42 \text{ cubic meters} \]

### Step 2: Identify the Base Dimensions
The base dimensions of the reservoir are given as:
- Length (L) = 6 meters
- Breadth (B) = 3.5 meters

### Step 3: Use the Volume Formula
The volume (V) of a rectangular prism (like our reservoir) is calculated using the formula:
\[ V = L \times B \times H \]
Where:
- \( V \) = Volume
- \( L \) = Length
- \( B \) = Breadth
- \( H \) = Height (or Depth in this case)

### Step 4: Rearrange the Formula to Find Depth
We need to find the depth (H), so we rearrange the formula:
\[ H = \frac{V}{L \times B} \]

### Step 5: Substitute the Values
Now we can substitute the known values into the formula:
\[ H = \frac{42}{6 \times 3.5} \]

### Step 6: Calculate the Base Area
Calculate the area of the base:
\[ 6 \times 3.5 = 21 \text{ square meters} \]

### Step 7: Calculate the Depth
Now substitute the area back into the equation for depth:
\[ H = \frac{42}{21} = 2 \text{ meters} \]

### Conclusion
The depth of water in the reservoir is **2 meters**.

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