2 cm of rain has fallen on a square km of land. Assuming that `50%` of the raindrops could have been collected and contaied in a pool having a `100 m xx 10m` base, by what level would the water level in the pool have increased ?

Options

A. 1km
B. 10m
C. 10cm
D. 1m

Answer

To solve the problem step by step, we will follow these calculations:

### Step 1: Calculate the volume of rainwater that fell on the land.
- **Given**:
- Rainfall = 2 cm
- Area of land = 1 square kilometer = \(1,000,000 \, \text{m}^2\)

- **Convert the rainfall from cm to meters**:
\[ 2 \, \text{cm} = \frac{2}{100} \, \text{m} = 0.02 \, \text{m} \]

- **Calculate the volume of rainwater**:
\[ \text{Volume} = \text{Area} \times \text{Height} = 1,000,000 \, \text{m}^2 \times 0.02 \, \text{m} = 20,000 \, \text{m}^3 \]

### Step 2: Calculate the volume of rainwater that can be collected.
- **Given**:
- Only 50% of the rainwater can be collected.

- **Calculate the collected volume**:
\[ \text{Collected Volume} = 50\% \text{ of } 20,000 \, \text{m}^3 = \frac{1}{2} \times 20,000 = 10,000 \, \text{m}^3 \]

### Step 3: Calculate the volume of the pool.
- **Given**:
- Dimensions of the pool = 100 m x 10 m

- **Calculate the area of the base of the pool**:
\[ \text{Area of the base} = 100 \, \text{m} \times 10 \, \text{m} = 1,000 \, \text{m}^2 \]

### Step 4: Calculate the increase in water level in the pool.
- **Using the formula for volume**:
\[ \text{Volume} = \text{Area} \times \text{Height} \]
- We know the volume of the collected rainwater and the area of the pool, so we can find the height \(h\):
\[ 10,000 \, \text{m}^3 = 1,000 \, \text{m}^2 \times h \]
- **Solving for \(h\)**:
\[ h = \frac{10,000 \, \text{m}^3}{1,000 \, \text{m}^2} = 10 \, \text{m} \]

### Final Answer:
The water level in the pool would have increased by **10 meters**.

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