A river 3m deep and 40 m wide is flowing at the rate of 2 km per hour. How much water (in litres) 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, we need to calculate the volume of water flowing in the river per minute and then convert that volume into liters.

### Step-by-Step Solution:

1. **Identify the dimensions of the river:**
- Depth (height) of the river = 3 m
- Width of the river = 40 m

2. **Convert the speed of the river from km/h to m/min:**
- Speed of the river = 2 km/h
- To convert km/h to m/min, we use the conversion factor:
\[ 1 \text{ km} = 1000 \text{ m}, \quad 1 \text{ hour} = 60 \text{ minutes} \]
- Therefore,
\[ 2 \text{ km/h} = 2 \times 1000 \text{ m/h} = 2000 \text{ m/h} \]
- Now convert hours to minutes:
\[ 2000 \text{ m/h} \div 60 \text{ min/h} = \frac{2000}{60} \text{ m/min} = \frac{100}{3} \text{ m/min} \]

3. **Calculate the volume of water flowing per minute:**
- The volume \( V \) of water flowing in the river per minute can be calculated using the formula:
\[ V = \text{Length} \times \text{Width} \times \text{Height} \]
- Here, the length is the distance the water flows in one minute, which we calculated as \( \frac{100}{3} \) m.
- Thus,
\[ V = \left(\frac{100}{3} \text{ m}\right) \times (40 \text{ m}) \times (3 \text{ m}) \]

4. **Perform the multiplication:**
- Calculate the volume:
\[ V = \frac{100}{3} \times 40 \times 3 = \frac{100 \times 40 \times 3}{3} \]
- The \( 3 \) in the numerator and denominator cancels out:
\[ V = 100 \times 40 = 4000 \text{ m}^3 \]

5. **Convert the volume from cubic meters to liters:**
- We know that \( 1 \text{ m}^3 = 1000 \text{ liters} \).
- Therefore,
\[ 4000 \text{ m}^3 = 4000 \times 1000 \text{ liters} = 4,000,000 \text{ liters} \]

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