A river 3 m deep and 60 m wide is flowing at the rate of 2.4 km/h . The amount of water running into the sea per minute is :

Options

A. `6000 m^(3) `
B. `6400 m^3`
C. `6800 m^(3) `
D. `7200 m^(3) `

Answer

To find the amount of water running into the sea per minute from the river, we can follow these steps:

### Step 1: Convert the speed of the river from km/h to m/min
The speed of the river is given as 2.4 km/h. We need to convert this to meters per minute.

1 km = 1000 meters, and 1 hour = 60 minutes.

So, we convert:
\[ \text{Speed in m/min} = 2.4 \, \text{km/h} \times \frac{1000 \, \text{m}}{1 \, \text{km}} \times \frac{1 \, \text{h}}{60 \, \text{min}} = \frac{2400 \, \text{m}}{60 \, \text{min}} = 40 \, \text{m/min} \]

### Step 2: Calculate the cross-sectional area of the river
The river has a depth of 3 meters and a width of 60 meters. The cross-sectional area (A) can be calculated as:
\[ A = \text{width} \times \text{depth} = 60 \, \text{m} \times 3 \, \text{m} = 180 \, \text{m}^2 \]

### Step 3: Calculate the volume of water flowing per minute
The volume of water flowing per minute (V) can be calculated using the formula:
\[ V = \text{cross-sectional area} \times \text{speed} \]
Substituting the values we have:
\[ V = 180 \, \text{m}^2 \times 40 \, \text{m/min} = 7200 \, \text{m}^3/\text{min} \]

### Conclusion
The amount of water running into the sea per minute is **7200 m³/min**.

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