Water in a canal 3 m wide and 1.2 m deep,is flowing with the velocity of 10 km/h. how mucharea (in hectares) will it irrigate in half an hour, if 9 cm of standing water is needed?

Options

A. 20
B. 18.8
C. 21
D. 20.4

Answer

To solve the problem, we need to determine how much area can be irrigated by the water flowing in the canal, given the dimensions of the canal and the requirement for standing water.

### Step-by-Step Solution:

1. **Calculate the Volume of Water Flowing in the Canal:**
- The formula for the volume of water flowing in a canal is given by:
\[ \text{Volume} = \text{Area of cross-section} \times \text{Velocity} \times \text{Time} \]
- The area of the cross-section of the canal can be calculated as:
\[ \text{Area} = \text{Width} \times \text{Depth} = 3 \, \text{m} \times 1.2 \, \text{m} = 3.6 \, \text{m}^2 \]
- Convert the velocity from km/h to m/s:
\[ 10 \, \text{km/h} = \frac{10 \times 1000}{3600} \, \text{m/s} = \frac{10000}{3600} \approx 2.78 \, \text{m/s} \]
- Time in seconds for half an hour:
\[ \text{Time} = 30 \, \text{minutes} = 30 \times 60 = 1800 \, \text{s} \]
- Now calculate the volume of water:
\[ \text{Volume} = 3.6 \, \text{m}^2 \times 2.78 \, \text{m/s} \times 1800 \, \text{s} \approx 18000 \, \text{m}^3 \]

2. **Calculate the Area that can be Irrigated:**
- We need to find out how much area can be irrigated with 9 cm of standing water. First, convert 9 cm to meters:
\[ 9 \, \text{cm} = 0.09 \, \text{m} \]
- The area that can be irrigated is given by:
\[ \text{Area} = \frac{\text{Volume}}{\text{Height of standing water}} = \frac{18000 \, \text{m}^3}{0.09 \, \text{m}} = 200000 \, \text{m}^2 \]

3. **Convert the Area from Square Meters to Hectares:**
- 1 hectare = 10,000 m², so:
\[ \text{Area in hectares} = \frac{200000 \, \text{m}^2}{10000 \, \text{m}^2/\text{hectare}} = 20 \, \text{hectares} \]

### Final Answer:
The area that can be irrigated in half an hour is **20 hectares**.