A river 2 m deep and 45 m wide is running at the rate of 3 km/hr. The amount of water that runs into the sea per minute is---

Options

A. `4500 m^3`
B. `27000 m^3`
C. `3000 m^3`
D. `2100 m^3`

Answer

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

### Step 1: Calculate the Cross-Sectional Area of the River
The cross-sectional area (A) of the river can be calculated using the formula:
\[ A = \text{width} \times \text{depth} \]
Given:
- Width = 45 m
- Depth = 2 m

So,
\[ A = 45 \, \text{m} \times 2 \, \text{m} = 90 \, \text{m}^2 \]

### Step 2: Convert the Speed of the River from km/hr to m/min
The speed of the river is given as 3 km/hr. We need to convert this speed into meters per minute.
1 km = 1000 m and 1 hour = 60 minutes.
So,
\[ \text{Speed in m/min} = 3 \, \text{km/hr} \times \frac{1000 \, \text{m}}{1 \, \text{km}} \times \frac{1 \, \text{hr}}{60 \, \text{min}} \]
Calculating this gives:
\[ \text{Speed in m/min} = 3 \times \frac{1000}{60} = 50 \, \text{m/min} \]

### Step 3: Calculate the Volume of Water Flowing Per Minute
The volume of water flowing per minute (V) can be calculated using the formula:
\[ V = \text{Area} \times \text{Speed} \]
Substituting the values we have:
\[ V = 90 \, \text{m}^2 \times 50 \, \text{m/min} \]
Calculating this gives:
\[ V = 4500 \, \text{m}^3/\text{min} \]

### Conclusion
The amount of water that runs into the sea per minute is **4500 m³**.

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