A river 3 m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water in liters )will fall into the sea in a minute?

Options

A. 4,00,000
B. 40,00,000
C. 40000
D. 4000

Answer

To solve the problem of how much water will fall into the sea from the river in one minute, we can follow these steps:

### Step 1: Understand the dimensions of the river
We know that the river is:
- Depth = 3 meters
- Width = 40 meters

### Step 2: Calculate the cross-sectional area of the river
The cross-sectional area (A) can be calculated using the formula:
\[ A = \text{Depth} \times \text{Width} \]
\[ A = 3 \, \text{m} \times 40 \, \text{m} = 120 \, \text{m}^2 \]

### Step 3: Determine the flow rate of the river
The river flows at a speed of 2 km/h. We need to convert this speed into meters per second (m/s) for easier calculations:
\[ 2 \, \text{km/h} = \frac{2 \times 1000 \, \text{m}}{3600 \, \text{s}} = \frac{2000}{3600} \approx 0.5556 \, \text{m/s} \]

### Step 4: Calculate the volume of water flowing in one second
The volume of water flowing in one second (V) can be calculated using the formula:
\[ V = A \times \text{Flow Rate} \]
\[ V = 120 \, \text{m}^2 \times 0.5556 \, \text{m/s} \approx 66.67 \, \text{m}^3/\text{s} \]

### Step 5: Calculate the volume of water flowing in one minute
To find the volume of water flowing in one minute, we multiply the volume per second by 60:
\[ V_{\text{1 minute}} = 66.67 \, \text{m}^3/\text{s} \times 60 \, \text{s} = 4000 \, \text{m}^3 \]

### Step 6: Convert cubic meters to liters
Since 1 cubic meter is equivalent to 1000 liters, we can convert the volume:
\[ V_{\text{liters}} = 4000 \, \text{m}^3 \times 1000 \, \text{liters/m}^3 = 4,000,000 \, \text{liters} \]

### Final Answer
Thus, the amount of water that will fall into the sea in one minute is **4,000,000 liters**.

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