A rectangular water reservoir contains 42000 litres of water. If the length of reservoir is 6 m and its breadth is 3.5 m. The depth of the reservoir is

Options

A. 2m
B. 5m
C. 6m
D. 8m

Answer

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

### Step 1: Convert the volume from liters to cubic meters
The volume of the reservoir is given as 42,000 liters. We know that:
1 liter = 0.001 cubic meters.

So, we convert 42,000 liters to cubic meters:
\[ \text{Volume in cubic meters} = 42000 \times 0.001 = 42 \, \text{m}^3 \]

### Step 2: Write down the formula for the volume of a cuboid
The volume \( V \) of a cuboid (rectangular prism) is given by the formula:
\[ V = \text{length} \times \text{breadth} \times \text{height} \]
In this case, the height is the depth of the reservoir.

### Step 3: Substitute the known values into the volume formula
We have:
- Length \( l = 6 \, \text{m} \)
- Breadth \( b = 3.5 \, \text{m} \)
- Volume \( V = 42 \, \text{m}^3 \)

Substituting these values into the formula gives:
\[ 42 = 6 \times 3.5 \times h \]

### Step 4: Calculate the product of length and breadth
First, calculate \( 6 \times 3.5 \):
\[ 6 \times 3.5 = 21 \]

### Step 5: Rearrange the equation to solve for height (depth)
Now, we can rearrange the equation to find \( h \):
\[ h = \frac{V}{l \times b} = \frac{42}{21} \]

### Step 6: Calculate the height (depth)
Now, calculate \( h \):
\[ h = \frac{42}{21} = 2 \, \text{m} \]

### Conclusion
The depth of the reservoir is \( 2 \, \text{m} \).

---